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
In case you have suggestions for topics or willing
to speak please contact Rami@cmu.edu