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