Logic seminar, Fall 2013


This semester the topic component to the logic seminar will focus on topics related to proper forcing. The papers presented in this part of the seminar are grouped into clusters, with some background presented leading up to the main result.

The following references provide background and motivation on proper forcing:
S. Shelah, Proper and Improper Forcing, 2nd edition. Perspectives in Mathematical Logic, Volume 5 Springer-Verlag: Berlin (1998), 1020 pp. This is the original source on proper forcing.
J. Tatch Moore, A tutorial on the Proper Forcing Axiom 2010 Young Set Theory Meeting, Raach, Austria (notes by Giorgio Venturi). This contains the basics on applying the proper forcing axiom, complete with proofs that PFA implies OCA and PID.
J. Tatch Moore, The Proper Forcing Axiom Proceedings of the 2010 meeting of the ICM. pp. 3--29 This is an expository article, motivating the proper forcing axiom.
T. Eisworth, D. Milovich, J. Tatch Moore, Iterated forcing and the Continuum Hypothesis in Appalachian set theory 2006-2012, J. Cummings and E. Schimmerling, eds. London Math Society Lecture Notes series, Cambridge University Press (2013). This contains a proof that a countable support iteration of proper forcings is proper. It also contains information on obtaining models of CH by iterated proper forcing.

The first pair of papers which will be presented in the seminar will be:
[M1] J. Tatch Moore, Set mapping reflection Journal of Mathematical Logic, 5 (2005), n 1, pp. 87-98.
[IM] T. Ishiu, J. Tatch Moore, Minimality of non \(\sigma\)-scattered orders Fundamenta Mathematicae. 205 (2009), n 1, pp. 29--44.
The following contains some additional reading: D. Milovich, J. Moore, A tutorial on Set Mapping Reflection in Appalachian set theory 2006-2012, J. Cummings and E. Schimmerling, eds. London Math Society Lecture Notes series, Cambridge University Press (2013).

The second cluster will some introductory material on iterating proper forcing without adding reals (see AST notes for the Eisworth-Moore tutorial above) followed by:
[M2] J. Tatch Moore, \(\omega_1\) and \(-\omega_1\) may be the only minimal uncountable order types Michigan Math. Journal 55 (2007), n 2, pp. 437--457.

Fall 2013 talks:

Tuesday, 9/3: Brooks' theorem on standard probability spaces
  Clinton Conley, Cornell University

Wednesday, 9/4: no seminar (fall reception)



Tuesday, 9/10: Brooks' theorem on standard probability spaces, part II
  Clinton Conley, Cornell University

Wednesday, 9/11: An introduction to proper forcing
  Justin Moore, Cornell University



Tuesday, 9/17: (canceled)

Wednesday, 9/18: An introduction to proper forcing, part II
  Justin Moore, Cornell University



Tuesday, 9/24: Finite forms of Gowers' Theorem on the oscillation stability of \(c_0\)
  Diana Ojeda, Cornell University

Wednesday, 9/25: Iterated proper forcing
  Justin Moore, Cornell University



Tuesday, 10/1: Saturated models and disjunctions in second-order arithmetic
  David Belanger, Cornell University

Wednesday, 10/2: Set Mapping Reflection
  David Belanger, Cornell University



Tuesday, 10/8: TBA
  Adam Bjorndahl, Cornell University

Wednesday, 10/9: Minimal non \(\sigma\)-scattered linear orders
  Hossein Lamei Ramandi, Cornell University



Tuesday, 10/15: no seminar (fall break)

Wednesday, 10/16: Minimal non \(\sigma\)-scattered linear orders, part II
  Hossein Lamei Ramandi, Cornell University



Tuesday, 10/22: Devlin and Shelah's weak diamond principle
  Jeffrey Bergfalk, Cornell University

Wednesday, 10/23: Games and Borel graph colorings
  Andrew Marks, Caltech



Tuesday, 10/29: Continuous automata over a compact alphabet
  Scott Messick, Cornell University

Wednesday, 10/30: Introduction to iterated totally proper forcing
  Justin Moore, Cornell University



Tuesday, 11/5: The Open Coloring Axiom
  Iian Symthe, Cornell University

Wednesday, 11/6: \(\omega_1\) and \(-\omega_1\) may be the only minimal uncountable linear orders
  Jeffrey Bergfalk, Cornell University



Tuesday, 11/12: PFA and automorphsisms of \(\mathcal{P}(\mathbb{N})/\mathrm{fin}\), part I
  Iian Smythe, Cornell University

Wednesday, 11/13: \(\omega_1\) and \(-\omega_1\) may be the only minimal uncountable linear orders, part II
  Jeffrey Bergfalk, Cornell University



Tuesday, 11/19: The P-ideal Dichotomy
  Diana Ojeda, Cornell University

Wednesday, 11/20: PFA implies PID
  Justin Moore, Cornell University



Tuesday, 11/26: PFA implies OCA
  Iian Smythe, Cornell University

Wednesday, 11/27: no seminar (Thanksgiving break)



Tuesday, 12/3: Memoryless determinacy of parity games
  Tom Kern, Cornell University

Wednesday, 12/4: The consistency of the Proper Forcing Axiom, part I
  Scott Messick, Cornell University



Wednesday, 12/11: The consistency of the Proper Forcing Axiom, part II
  Scott Messick, Cornell University

Thursday, 12/12: Linear orders \(L\) satisfying \(L^n = L\)
  Garrett Ervin, University of California, Irvine