Model Theory Seminar
M 3:30 - 6:00 PM
Wean 6423

• November 17, 2004
SPEAKER: Spas Bojanov, CMU
TITLE: Categoricity theorem for uncountable firt-order theories. Part 1
ABSTRACT: Sh31. This is the paper were Shelah presents his proof for Morley's theorem for uncountable theories:
THEOREM Let T be a first-order theory. If T is categorical in a cardinal greater than |T|+\aleph_0 then it is categorical in all cardinals greater than |T|+\aleph_0.
This paper is fundamental to model theory as it introduces several important concepts. Baldwin in his detailed review of this paper for MR wrote "The proof is a miracle of localization".
While Shelah's paper is not self contained, the lectures will assume familiarity of only an introductory course in model theory as last year's 21-603.
• Nov. 22, 2004
SPEAKER: Spas Bojanov, CMU
TITLE:Categoricity theorem for uncountable firt-order theories. Part 2
• Nov. 30, 2004
SPEAKER: Spas Bojanov, CMU
TITLE:Categoricity theorem for uncountable firt-order theories. Part 3
• Dec 1, 2004
SPEAKER: Spas Bojanov, CMU
TITLE:Categoricity theorem for uncountable firt-order theories. Part 4
• Dec. 8, 2004
SPEAKER: Spas Bojanov, CMU
TITLE:Categoricity theorem for uncountable firt-order theories. Part 5
• Dec. 8, 2004
SPEAKER: Spas Bojanov, CMU
TITLE:Categoricity theorem for uncountable firt-order theories. Part 6

• Feb. 21, 2005
SPEAKER: Peter Glenn, CMU
TITLE: An introduction to the model theory of L_omega1,omega. Part 1
ABSTRACT: L_omega1,omega is a fragment of second-order logic which is well behaved model theoretically and in recent years got increased attention due to its expressive power and the connection between L\omega1,\omega(Q) and Schanuell's conjecture in transcendental number theory. The prerequisites for Glenn's talks are only a basic logic course, familiarity of the contents of Model Theory I (21-603) is not assumed.
• Feb. 28, 2005
SPEAKER: Peter Glenn, CMU
TITLE: An introduction to the model theory of L_omega1,omega. Part 2
• March 7, 2005
SPEAKER: Peter Glenn, CMU
TITLE: An introduction to the model theory of L_omega1,omega. Part 2
• March 7, 2005
SPEAKER: Peter Glenn, CMU
TITLE: An introduction to the model theory of L_omega1,omega. Part 3

• March 14, 2005
SPEAKER: Spas Bojanov, CMU
TITLE: Superstable fields are algebraically closed, Part 1
ABTRACT: The main result of Cherlin and Shelah's "Superstable fields and groups"- paper will be proved. The proof is an application of rank functions from stability theory to stable fields groups. The lectures will be self contained and all relevant facts and definitions from Model theory will be presented.
• March 21, 2005
SPEAKER: Spas Bojanov, CMU
TITLE: Superstable fields are algebraically closed, Part 2
• March 28, 2005
SPEAKER: Spas Bojanov, CMU
TITLE: Superstable fields are algebraically closed, Part 3

• April 11, 2005
SPEAKER: Peter Glenn, CMU
TITLE: Constructing many non-isomorphic models in \aleph_1", Part 1
ABSTRACT: The goal of this sequence of talks will be to prove:
THEOREM (Keisler). If an L_\omega_1,\omega theory has a model realizing uncountable many types over a fixed countable fragment then the theory has 2^{\aleph_1}-many pairwise non-isomorphic models of cardinality \aleph_1.
The proof require an omitting-types theorem and a theorem about end-extensions of countable models. Both are results of independent importance and interest.
• April 18, 2005
SPEAKER: Peter Glenn, CMU
TITLE: Constructing many non-isomorphic models in \aleph_1", Part 2
• April 25, 2005
SPEAKER: Peter Glenn, CMU
TITLE: Constructing many non-isomorphic models in \aleph_1", Part 3