Most of the documents below with electronic versions have been compiled for optimum viewing in PDF format. However, some papers (for various reasons) look grainy as PDF files. All the papers with electronic versions are, however, also available in postscript and DVI format.

- On large cardinals and partition relations,
*Journal of Symbolic Logic***36**(1971), 305-308 (with E.M. Kleinberg). - Weak compactness and square bracket partition relations,
*Journal of Symbolic Logic***37**(1972), 673-676 (with E.M. Kleinberg). - Square bracket partition relations in
*L*,*Fundamenta Mathematica***34**(1974), 101-106. - Minimal alpha-degrees,
*Annals of Mathematical Logic***4**(1972), 383-414. - Cohesive sets: countable and uncountable,
*Proceedings of the American Mathematical Society***44**(1974), 442-445. - Sigma
_{n}sets which are Delta_{n}-incomparable (uniformly),*Journal of Symbolic Logic***39**(1974), 295-304. - Splitting an alpha-recursively enumerable set,
*Transactions of the American Mathematical Society***204**(1975), 65-77. - The recursively enumerable alpha-degrees are dense,
*Annals of Mathematical Logic***9**(1976), 123-155. - The irregular and non-hyperregular alpha-r.e. degrees,
*Israel Journal of Mathematics***22**(1975), 28-41. - On the jump of an alpha-recursively enumerable set,
*Transactions of the American Mathematical Society***217**(1976), 351-363. - Types of simple alpha-recursively enumerable sets,
*Journal of Symbolic Logic***41**(1976), 681-693 (with A. Leggett). - alpha-Recursion theory, in
*Handbook of Mathematical Logic*, J.Barwise ed., North-Holland, 1977, 653-680. - Determining automorphisms of the recursively enumerable sets,
*Proceedings of the American Mathematical Society***65**(1977), 318-325. - Controlling the dependence degree of a recursively enumerable vector
space,
*Journal of Symbolic Logic***43**(1978), 13-22. - Some more minimal pairs of alpha-recursively enumerable degrees,
*Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik***24**(1978), 409-418. - Nowhere simple sets and the lattice of recursively enumerable sets,
*Journal of Symbolic Logic***43**(1978), 322-330. - On the AE-sentences of alpha-recursion theory, in
*Generalized Recursion Theory II*, Fenstad, Gandy and Sacks, eds., North-Holland 1978, 331-354. *r*-Maximal major subsets,*Israel Journal of Mathematics***31**(1978), 1-18 (with M. Lerman and R.I. Soare).- Second order logic and first order theories of reducibility orderings in
*The Kleene Symposium*, J. Barwise, H.J. Keisler and K. Kunen, eds., North- Holland, 1980, 181-200 (with A. Nerode). - Reducibility orderings: theories, definability and automorphisms,
*Annals of Mathematical Logic***18**(1980), 61-89 (with A. Nerode). - The homogeneity conjecture,
*Proceedings of the National Academy of Sciences***76**(1979), 4218-4219. - On homogeneity and definability in the first order theory of the Turing
degrees,
*Journal of Symbolic Logic***47**(1982), 8-16. *L*^{*}(*K*) and other lattices of recursively enumerable sets,*Proceedings of the American Mathematical Society***80**(1980), 143-146.- Some constructions in alpha-recursion theory, in
*Recursion Theory: Its Generalizations and Applications*, F.R. Drake and S.J. Wainer, eds., London Mathematical Society Lecture Notes Series, no. 45, Cambridge University Press, Cambridge, England, 1980, 158-170. - The theory of the degrees below
**0**',*Journal of the London Mathematical Society***24**(1981), 1-14. - The elementary theory of the recursively enumerable degrees is not
aleph
_{0}-categorical,*Advances in Mathematics***53**(1984), 301-320 (with M. Lerman and R.I. Soare). - Splitting properties and jump classes,
*Israel Journal of Mathematics***39**(1981), 210-224 (with W. Maass and M. Stob). - Definable degrees and automorphisms of
*D*,*Bulletin of the American Mathematical Society**(NS)***4**(1981), 97-100 (with L. Harrington). - The degrees of unsolvability: global results, in
*Logic Year 1980-81: The University of Connecticut*, M. Lerman, J. Schmerl and R. Soare, eds., Springer- Verlag, 1981, 283-301. - Finitely generated codings and the degrees r.e. in a degree
**d**,*Proceedings of the American Mathematical Society***84**(1982), 256-263. - The Turing and truth-table degrees are not elementarily equivalent, in
*Logic Colloquium 1980*, D. van Dalen, D. Lascar and T.J. Smiley, eds., North-Holland, Amsterdam 1982, 231-237. - An algebraic decomposition of the recursively enumerable degrees and the
coincidence of several degree classes with the promptly simple degrees,
*Transactions of the American Mathematical Society***281**(1984), 109-128 (with K. Ambos-Spies, C. Jockusch and R. Soare). - Pseudo-jump operators I: the r.e. case,
*Transactions of the American Mathematical Society***275**(1983), 599-610 (with C. Jockusch). - Pseudo-jump operators II: transfinite iterations hierarchies and minimal
covers,
*Journal of Symbolic Logic***49**(1984), 1205-1236 (with C. Jockusch). - The arithmetical degrees are not elementarily equivalent to the Turing
degrees,
*Archiv fur Mathematische Logik und Grundlagenforschung***24**(1984), 137-139. - The degrees of unsolvability: the ordering of functions by relative
computability, in
*Proceedings*of the*International Congress of Mathematicians (Warsaw) 1983*, PWN-Polish Scientific Publishers, Warsaw 1984, Vol. 1, 337-346. *Recursion Theory, Proceedings of the Symposia in Pure Mathematics*, Vol. 42 (Proceedings of the AMS-ASL Summer Institute on Recursion Theory, Cornell, 1982), American Mathematical Society, Providence, R.I., 1985 (edited with A. Nerode).- The structure of the degrees of unsolvability, in
*Recursion Theory, Proceedings of the Symposia in Pure Mathematics***42**, A. Nerode and R.A. Shore, eds., American Mathematical Society,Providence, R.I., 1985, 33-51. - REA operators, r.e. degrees and minimal covers, in Recursion
*Theory, Proceedings of the Symposia in Pure Mathematics***42**, A. Nerode and R.A. Shore, eds., American Mathematical Society,Providence, R.I., 1985, 3-11 (with C. Jockusch). - Embeddings and extensions of embeddings in the r.e. tt and wtt
degrees, in
*Proceedings of the Oberwolfach "Recursion Theoretic Week 1984"*, H.D. Ebbinghaus, G.H. Müller and G.E. Sacks, eds., Springer-Verlag, Berlin, 1985, 121-140 (with P. Fejer). - Recursive limits on the Hahn-Banach theorem,
*Contemporary Mathematics***39**(1985), 85-91 (with A. Nerode and G. Metakides). - Initial segments of the Turing degrees of size aleph
_{1},*Israel Journal of Mathematics***55**(1986), 1-51 (with U. Abraham). - The degrees of constructibility below a Cohen real,
*Journal of the London Mathematical Society (3)***53**(1986), 193-208 (with U. Abraham). - Infima of recursively enumerable truth table degrees,
*Notre Dame Journal of Formal Logic***29**(1988), 420-437 (with P. Fejer). - A non-inversion theorem for the jump operator,
*Annals of Pure and Applied Logic***40**(1988), 277-303. - Decidability and invariant classes for degree structures,
*Transactions of the American Mathematical Society***310**(1988), 669-692 (with M. Lerman). - Defining jump classes in the degrees below
**0**',*Proceedings of the American Mathematical Society***104**(1988), 287-292. - Initial segments of the degrees of constructibility,
*Israel Journal of Mathematics, Israel Journal of Mathematics***63**(1988), 149-177 (with M. Groszek). - The
*p-T*-degrees of the recursive sets: lattice embeddings, extension of embeddings and the two quantifier theory (extended abstract), in*Proceedings: Structures in Complexity Theory, 4*, Comp. Soc. IEEE, 1989 (with T. Slaman).^{th}Annual Conference - A direct construction of a minimal recursively enumerable truth-table
degree, in
*Recursion Theory Week, Proceedings Oberwolfach 1989*, K. Ambos-Spies, G. H. Muller and G. E. Sacks, eds. Springer-Verlag,*LNMS***1432**(1990), 187-204 (with P. Fejer). - Undecidability and initial segments of the (r.e.) tt-degrees,
*Journal of Symbolic Logic***55**(1990), 987-1006 (with C. Haught). - Working below a low
_{2}recursively enumerable degrees,*Archive for Mathematical Logic***29**(1990), 201-211 (with T. Slaman). - Undecidability and initial segments of the wtt-degrees below
**0**', in*Recursion Theory Week, Proceedings Oberwolfach 1989*, K. Ambos-Spies, G. H. Muller and G. E. Sacks, eds. Springer-Verlag,*LNMS***1432**(1990), 223-244 (with C. Haught). - Global properties of local structures of degrees,
*Bul. U. Mat. Ital.***7**(1991), 97-120 (with G. Odifreddi). - On the strength of König's duality theorem for infinite bipartite
graphs,
*Journal of Combinatorial Theory (B)***54**(1992), 257-290 (with R. Aharoni and M. Magidor). - The
*p-T*-degrees of the recursive sets: lattice embeddings, extension of embeddings and the two quantifier theory,*Theoretical Computer Science***97**(1992), 263-284 (with T. Slaman). - Working below a high recursively enumerable degree,
*Journal of Symbolic Logic***58**(1993), 824-859 (with T. Slaman). - Degrees of constructibility, in
*Set theory of the Continuum*, H. Judah, W. Just and H. Woodin eds.,*MSRI Publications***26**, Springer-Verlag, Berlin, 1992, 123-135. - The
*n*-r.e.a. enumeration degrees are dense,*Archive for Mathematical Logic***31**(1992), 227-285 (with A. Lachlan). - The theory of the recursively enumerable weak truth table degrees is
undecidable,
*Journal of Symbolic Logic***57**(1992), 864-874 (with Ambos-Spies and Nies). - Countable thin Pi
_{1}^{0}classes,*Annals of Pure and Applied Logic***59**(1993) 79-139 (with D. Cenzer, R. Downey and C. Jockusch).

Also available in postscript or DVI format. - Undecidability and 1-types in the r.e. degrees,
*Annals of Pure and Applied Logic***63**(1993), 3-37 (with K. Ambos-Spies). - On the strength of Fraïssé's conjecture, in
*Logical Methods*, J. N. C. Crossley, J. Remmel, R. A. Shore and M. Sweedler, eds., Birkhäuser, Boston, 1993, 782-813. - Interpreting true arithmetic in the theory of the r.e. truth table
degrees,
*Annals of Pure and Applied Logic*,**75**(1995), 269-311 (with A. Nies). - Degree theoretic definitions of the
low
_{2}r. e. sets,*Journal of Symbolic Logic***60**(1995), 727-756 (with R. Downey).

Also available in postscript or DVI format. - Jumps of minimal degrees below
**0**',*Journal of the London Mathematical Society***60**(1995), 727-756 (with R. Downey and S. Lempp).

Also available in postscript or DVI format. - Highness and bounding minimal pairs,
*Mathematical Logic Quarterly***39**(1993), 475-491 (with R. Downey and S. Lempp)

Also available in postscript or DVI format. - The theories of the T, tt and wtt r.e.
degrees: undecidability and beyond, in
*Proc. IX Latin American Symposium on Mathematical Logic (part 1)*, Notas de Lo'gica Mathema'tica**38**, Universidad Nacional del Sur, Bahia Blanca, Argentina, 1993, 61-70.

Also available in postscript or DVI format. *Logical Methods: In Honor of Anil Nerode's Sixtieth Birthday*, Birkäuser, Boston, Mass., 1993 (edited with J. N. C. Crossley, J. Remmel and M. Sweedler).*Logic for Applications*, Texts and Monographs in Computer Science, Springer-Verlag, New York, 1993 (with A. Nerode); 2^{nd}ed., Graduate Texts in Computer Science, Springer-Verlag, New York, 1997 (with A. Nerode).- Conjectures and questions from Gerald
Sacks's
*Degrees of Unsolvability*,*Archive for Mathematical Logic***36**(1997), 233-253.

Also available in postscript or DVI format. - Lattice embeddings below a
nonlow
_{2}recursively enumerable degree,*Israel Journal of Mathematics***94**(1996), 221-246 (with R. Downey).

Also available in postscript or DVI format. - Interpolating d-r.e. and REA degrees between
r.e. degrees,
*Annals of Pure and Applied Logic***78**(1996), 29-56 (with M. Arslanov and S. Lempp).

Also available in postscript or DVI format. - On isolating r.e. and isolated d-r.e.
degrees, in
*Computability, Enumerability, Unsolvability: Directions in Recursion Theory*, S. B. Cooper, T. A. Slaman and S. S. Wainer eds.,*LMSLN***224**, Cambridge University Press, Cambridge, England, 1996, 61-80 (with M. Arslanov and S. Lempp).

Also available in postscript or DVI format. - The recursively enumerable degrees,
in
*Handbook of Recursion Theory*, E. Griffor ed., North-Holland, Amsterdam, 1999, 169-197.

Also available in postscript or DVI format. - Intervals without critical triples,
in
*Logic Colloquium '95*, J. A. Makowsky and E. V. Ravve, eds.,*Lecture Notes in Logic***11**, Springer-Verlag, Heidelberg, 1998, 17-43 (with P. Cholak and R. Downey).

Also available in postscript or DVI format. - Definability in the recursively enumerable degrees,
*Bulletin of Symbolic Logic***2**(1996), 392-404, (with A. Nies and T. Slaman).

Also available in postscript or DVI format. - Computably categorical structures and
extensions by constants,
*Journal of Symbolic Logic*,**64**(1999), 13-37 (with P. Cholak, S. Goncharov and B. Khoussainov).

Also available in postscript or DVI format. - Computable models of theories with few
models,
*Notre Dame Journal of Formal Logic***38**(1997), 165-178 (with B. Khoussainov and A. Nies).

Also available in postscript or DVI format. - Splitting theorems and the jump operator,
*Annals of Pure and Applied Logic***94**(1997), 45-52 (with R. Downey).

Also available in postscript or DVI format. - There is no degree invariant half jump,
*Proc. Am Math. Soc.***125**(1997), 3033-3037 (with R. Downey).

Also available in postscript or DVI format. - Categoricity and Scott families,
extended abstract,
*Combinatorics, Complexity and Logic, Proceedings of DMTCS '96*, D. Bridges et al. eds., Springer-Verlag, Singapore, 1997, 299-308 (with B. Khoussainov).

Also available in postscript or DVI format. - Interpretability and definability in the
recursively enumerable degrees,
*Proc. Lon. Math. Soc.*(3)**77**(1998), 241-291 (with A. Nies and T. Slaman).

Also available in postscript or DVI format. - Computable Isomorphisms, Degree Spectra of
Relations, and Scott Families,
*Annals of Pure and Applied Logic***93**(1998), 153-193 (with B. Khoussainov).

Also available in postscript or DVI format.

Revised version in postscript or DVI format. - Undecidability and 1-types in
intervals of the c.e. degrees,
*Annals of Pure and Applied Logic***106**(2000), 1-48 (with K. Ambos-Spies and D. Hirschfeldt).

Also available in postscript or DVI format. - Jumps of Sigma2-high e-degrees
and properly Sigma2 e-degrees, in
*Recursion Theory and Complexity*, M. Arslanov and S. Lempp eds., de Gruyter Series in Logic and its Applications**2**, de Gruyter, Berlin, 1999, 157-172 (with A. Sorbi).

Also available in postscript or DVI format. - Effective model theory: the number of models
and their compelxity, in
*Models and Computability, Invited papers from Logic Colloquium '97*, S. B. Cooper and J. K. Truss eds., LMSLNS**259**, Cambridge University Press, Cambridge, England, 1999, 193-240 (with B. Khoussainov).

Also available in postscript or DVI format. - Every incomplete computably enumerable truth-table degree is branching,
*Archive for Mathematical Logic***40**(2001), 113-123 (with P. Fejer).

Also available in postscript or DVI format. - Reasoning about common knowledge with infinitely many agents,
*Information and Computation***191**(2004), 1-40 (with J. Halpern).

Also available in postscript as is the Extended abstract from the Proceedeings of LICS Meeting, Trento, Italy, July 1999 or DVI as is the Extended abstract from the Proceedeings of LICS Meeting, Trento, Italy, July 1999. - Solutions of the Goncharov-Millar and degree spectra problems in the
theory of computable models,
*Dokl. Akad. Nauk SSSR***371**(2000) 30--31 (Russian), English version:*Doklady Mathematics***61**(2000), 178-179 (with B. Khoussainov).

Also available in postscript or DVI format. - Decomposition and infima in the
computably enumerable degrees,
*Journal of Symbolic Logic*,**68**(2003), 551-579 (with R. Downey and G. Laforte).

Also available in postscript or DVI format. - Degree spectra and computable dimension
in algebraic structures,
*Annals of Pure and Applied Logic***115**(2002), 71-113 (with D. Hirschfeldt, B. Khoussainov and A. Slinko).

Also available in postscript or DVI format. - Natural definability in degree
structures, in
*Computability Theory and Its Applications: Current Trends and Open Problems*, P. Cholak, S. Lempp, M. Lerman and R. A. Shore eds.,*Contemporary Mathematics*, AMS, Providence RI, 2000, 255-272.

Also available in postscript or DVI format. - A splitting theorem for
n-REA degrees,
*Proc. American Mathematicl Society***129**(2001), 3721-3728 (with T. Slaman).

Also available in postscript or DVI format.

A follow up paper is A discrete splitting theorem for the 2-REA degrees (with T. Slaman).

Also available in postscript or DVI format. - Defining the Turing jump,
*Math. Research Letters***6**(1999), 711-722 (with T. Slaman).

Also available in postscript or DVI format. *Computability Theory and Its Applications: Current Trends and Open Problems*,*Contemporary Mathematics*, AMS, Providence RI, 2000 (edited with P. Cholak, S. Lempp and M. Lerman).- Computable Structures: Presentations Matter,
in
*In the scope of logic, methodology and the philosophy of science*}, Int. Congress of LMPS, Cracow, August 1999, P. Gardenfors, J. Wolenski and K. Kijania-Placek eds., Synthese Library**315**, Kluwer Academic Publishers, Dordrecht, 2002, vol. 1, 81-95.

Also available in postscript or DVI format. - A nonlow
_{2}r.e. degree with the extension of embeddings properties of a low_{2}degree,*Mathematical Logic Quarterly***6**(2002), no. 1 (with Y. Yang).

Also available in postscript or DVI - Intepreting arithmetic in the
r.e. degrees under ISigma-4-induction, in
*Reverse Mathematics 2001*, S. Simpson, ed., Lecture Notes in Logic**21**, Association for Symbolic Logic, 2005 (with C. T. Chong and Y. Yang). - The prospects for mathematical
logic in the twenty-first century,
*Bulletin of Symbolic Logic***7**(2001), 169-196 (with S. Buss, A. Kechris and A. Pillay).

Also available in postscript or DVI format. - The theory of the metarecursively enumerable
degrees,
*Journal of Mathematical Logic*,**6**(2006), 49-68 (with T. Slaman and N. Greenberg).

Also available in postscript or DVI format. - A computably categorical
structure whose expansion by a constant has infinite computable dimension,
*Journal of Symbolic Logic***68**(2003), 1199-1241 (with D. Hirschfeldt and B. Khoussainov).

Also available in postscript or DVI format. - Undecidability of the AE-theory of $\mathcal{R}(\leq
,\vee ,\wedge ),
*Transactions of the American Mathematical Society*,**356**(2004), 3025-3067 (with A. Nies and R. Miller).

Also available in postscript or DVI - Minimal degrees which are
Sigma_2 but not Delta_2,
*Proc. American Mathematicl Society***132**(2004), 563-565.

Also available in postscript or DVI format. - Pi^1_1 relations and paths
through O,
*Journal of Symbolic Logic***69**(2004), 585-611 (with S.S. Goncharov, V. Harizanov and J. Knight).

Also available in postscript or DVI format. - The AE theory of
$\mathcal{D}(\leq ,\vee ,^{\prime })$ is undecidable,
in Logic Colloquium '03, Viggo Stoltenberg-Hansen and Jouko Vaananen eds.,
Lecture Notes in Logic
**24**, ASL, ASL, 2006, 326-344 (with T.A. Slaman).

Also available in postscript or DVI format. - Generalized high degrees have the
complementatation property,
*Journal of Symbolic Logic***69**(2004), 1200-1220 (with N. Greenberg and A. Montalban).

Also available in postscript or DVI format. - Invariants, Boolean algebras and ACA_0^+ ,
*Transactions of the American Mathematical Society*,**358**(2006), 989-1014.

Also available in postscript or DVI format. - A computably stable structure with no Scott family of finitary
formulas,
*Archive for Mathematical Logic*,**45**(2006), 519-538 (with P. Cholak and R. Solomon).

Also available in postscript or DVI format. - Boolean Algebras,
Tarski Invariants, and Index Sets ,
*Notre Dame Journal of Formal Logic*,**47**(2006), 1-23 (with B. Csima and A. Montalban).

Also available in postscript or DVI format. - The low-n and low-m r.e. degrees are not
elementarily equivalent,
*Science in China A-Mathematics*,**47**(2004), 950-956.

Also available in postscript or DVI format. - Rigidity
and biinterpretability in the hyperdegrees, in
*Recursion Theory Worksphop:Proceedings of the IMS Program, Computational Prospects of Infinity*, C. T. Chong , F. Qi and Y. Yang eds., World Scientific Publishing Co., Singapore, 2008, 299-312.

Also available in postscript or DVI format. - Combinatorial principles weaker than Ramsey's
theorem for pairs,
*Journal of Symbolic Logic***72**(2007), 171-206 (with D. Hirschfeldt).

Also available in postscript or DVI format. - Degree Structures:
Local and Global Investigations,
*Bulletin of Symbolic Logic*,**12**(2006), 369-389.

Also available in postscript or DVI format. - The settling-time reducibility ordering,
*Journal of Symbolic Logic*,**72**(2007), 1055-71 (with B. Csima).

Also available in postscript or DVI format. - Direct and local defintions of the Turing
jump,
*Journal of Mathematical Logic***7**(2007), 229-262.

Also available in postscript or DVI format. - Local definability in degree structures:
the Turing jump, hyperdegrees and beyond,
*Bulletin of Symbolic Logic*,**13**(2007), 226-239.

Also available in postscript or DVI format. - Lattice initial segments of the hyperdegrees,
*Journal of Symbolic Logic***75**(2010), 103- 130 (with B. Kjos-Hanssen).

Also available in postscript or DVI format. - The atomic model theorem,
*Transactions of the American Mathematical Society*,**361**(2009), 5805-5837 (with D. Hirschfeldt and T. Slaman).

Also available in postscript or DVI format. - Domination, forcing, array nonrecursiveness and
relative recursive enumerability,
*Journal of Symbolic Logic*,**77**(2012), 226-239 (with M. Cai).

Also available in postscript DVI format. - Reverse mathematics, countable
and uncountable: a computational approach,
*Effective Mathematics of the Uncountable*, D. Hirschfeldt, N. Greenbergm J. D. Hamkins and R. Miller, eds., Lecture Notes in Logic, ASL and Cambridge University Press, New York, 2013, 150-163.

Also available in postscript or DVI format. - Topological aspects of
the Medvedev lattice,
*Archive for Mathematical Logic***50**(2011), 319-340 (with A. E. M. Lewis and A. Sorbi).

Also available in postscript or DVI format. - The limits of determinacy in second
order arithmetic
*Proceedings of the London Mathematical Society*,**104**(3) (2012), 223-252 (with A. Montalban).

Also available in postscript or DVI format. - Reverse Mathematics: the Playground of Logic,
*Bulletin of Symbolic Logic***16**(2010), 378-402.

Also available in postscript or DVI format. -
The n-r.e. degrees: undecidability and $\Sigma _{1}$ substructures,
*Journal of Mathematical Logic*,**12**(2012), 1-30 (with M. Cai and T. Slaman).

Also available in postscript or DVI format. -
The maximal linear extension theorem in second order arithmetic,
*Archive for Mathematical Logic***50**(2011), 543-564 (with A. Marcone).

Also available in postscript or DVI format. -
Degrees of categoricity and the hyperarithmetic hierarchy,
*Notre Dame Journal of Formal Logic*,**54**(2012), 215-232 (with B. F. Csima and J. Y. N. Franklin).

Also available in postscript -
Computably enumerable partial orders,
*Computability*,**1**(2012), 99-107 (with P. A. Cholak, D. D. Dzhafarov and N. Schweber).

Also available in postscript or DVI format. -
Biinterpretability up to double jump
in the degrees below 0',
*Proceedings of the American Mathematical Society*,**142**(2014), 351-360.

Also available in postscript or DVI format. -
The Turing Degrees: An Introduction, in
*Forcing, Iterated Ultrapowers, and Turing Degrees*, Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore**29**, eds. Chong Chi Tat, Feng Qi, Yang Yue, Theodore Slaman and Hugh Woodin, World Scientific Publishing, 2015, 39-121.

Also available in postscript or DVI format. -
Computing maximal chains,
*Archive for Mathematical Logic***51**(2012), 651-660 (with A. Marcone and A. Montalban).

Also available in postscript or DVI format. -
The complexity of ascendant sequences in locally nilpotent groups,
*International Journal of Algebra and Computation***24**(2014), 189-205 (with C. Conidis).

Also available in DVI format. -
Low level nondefinability results: domination and recursive enumeration,
*Journal of Symbolic Logic***78**(2013), 1005-1024 (with M. Cai).

Also available in postscript or DVI format. -
The Turing degrees below generics and randoms,
*Journal of Symbolic Logic*,**79**(2014), 171-178.

Also available in postscript or DVI format. -
The Limits of Determinacy in Second Order Arithmetic:
Consistency and Complexity Strength,
*Israel Journal of Mathematics*,**204**(2014), 477-508 (with A. Montalban).

Also available in postscript or DVI format. -
The Strength of Turing Determinacy within Second Order Arithmetic,
*Fundamenta Mathematica*,**232**(2016), 249-268 (with A. Montalban).

Also available in postscript or DVI format. -
*Induction, Bounding, Weak Combinatorial Principles, and The Homogeneous Model Theorem*,*Memoirs of the American Mathemactial Society***249**, American Mathematical Society, Providence, R.I. 2107, vi + 101 (with D. Hirschfeldt and K. Lange). Also available in postscript or DVI format. -
On the jumps of the degrees below an r.e. degree,
*Notre Dame Journal of Formal Logic*to appear (with D. Belanger).

Also available in postscript or DVI format. -
The strength of the Graetzer-Schmidt theorem,
*Archive for Mathematical Logic*,**55**(2016), 687-704 (with K. Brodhead, M. Khan, B. Kjos-Hansen, W A. Lampe and K. L. V. Nguyen).

Also available in postscript or DVI format. -
Mass problems and density,
*Journal of Mathematical Logic***16**(2016), 1650006 (with S. Binns and S. Simpson).

Also available in postscript or DVI format. -
Sigma ^1_1 in every real in a Sigma ^1_1 class of reals
is Sigma ^1_1, in
*Computability and Complexity, Essays Dedicated to Rodney Downey on the Occasion of His 60th Birthday*, A. Day, M. Fellows, N. Greenberg, B. Khoussainov, A. Melnikov and F. Rosamond eds., Springer-Verlag,**2017**, 455-468 (with L. Harrington and T. A. Slaman).

Also available in postscript or DVI format. -
Conservativity of ultrafilters over subsystems of second order arithmetic,
*Journal of Symbolic Logic*, to appear (with A. Montalban).

Also available in postscript or DVI format.

Richard Shore's Home Page