Rami Grossberg's WWW Page - CMU
I am working onthree volume model theory book series: · A course in Model Theory I: Introduction, 815 pages. · A course in Model Theory II: Classification Theory, 233pages. · A course in Model Theory III: Classification Theory forAbstract Elementary Classes, 205 pages.
www.math.cmu.edu
The purpose of this course is to present the basic concepts and techniques of model theory with an emphasis on pure model theory. The main theorem of the course is Morley's theorem. It will be presented in a way that permits several powerful extensions.
Abstract Classes. Abstract Elementary Classes. The major open questions concerning AEC. Shelah’s presentation Theorem and 2-categories. Basic Examples. PC-classes and omitting types. I(@0, K) = I(@1, K) =. Categoricity in = 1 =) @1 for AECs is K@2 not absolute ;. Random power set in higher order.
In this paper some of the basics of classification theory for abstract elementary classes are discussed. Instead of working with types which are sets of formulas (in the first-order case) we deal instead with Galois types which are essentially …
SUPERSTABILITY IN ABSTRACT ELEMENTARY CLASSES. RAMI GROSSBERG AND SEBASTIEN VASEY. Abstract. We prove that several de nitions of superstability in abstract elementary classes (AECs) are equivalent under the as-sumption that the class is tame, has amalgamation, joint embed-ding, and arbitrarily large models.
2 SAHARON SHELAH AND RAMI GROSSBERG In section 2 of [GrSh] we indicated that the proof of the main theo-rem can be adapted to give a result concerning cardinalities of inverse sys-tems of abelian groups subject to certain conditions (See Theorem 1.1 be-low). We did not include a proof there. Recently we were asked to sup-
RAMI GROSSBERG, MONICA VANDIEREN, AND ANDRES VILLAVECES´ Abstract. We prove: Theorem 0.1 (Main Theorem). Let K be an AEC and µ>LS(K). Suppose K satisfies the disjoint amalgamation property for models of cardinality µ. If K is µ …
Rami Grossberg Dept. of Math. Carnegie Mellon University Pittsburgh, PA 15213 August 4th, 1995 Abstract We prove some cool theorems on the border of Ramsey theory ( nite partition calculus) and model theory. Also a begining of clas-si cation theory for classes of nite models is attempted. Introduction
elementary classes proposed by Grossberg: Conjecture 6. For every cardinal µthere is µ 0 such that for all abstract elementary classes K with LS(K) ≤µ, if K is categorical in some λ 0 ≥µ 0, then K is categorical in all λ≥µ. While many special cases are verified (e.g. the case whereK is universal by Vasey
I would like to thank my advisor Prof. Rami Grossberg for his kind guidance and support. I would also like to thank the members of the thesis committee: Prof. John Baldwin, Prof. James Cummings, and Prof. Richard Statman for reading the thesis and for the many comments. Parts of this thesis were also read by Olivier Lessmann,
- Some results have been removed