Displaying similar documents to “Conservative extensions and the two cardinal theorem for stable theories”

Decompositions of saturated models of stable theories

M. C. Laskowski, S. Shelah (2006)

Fundamenta Mathematicae

Similarity:

We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.

The enriched stable core and the relative rigidity of HOD

Sy-David Friedman (2016)

Fundamenta Mathematicae

Similarity:

In the author's 2012 paper, the V-definable Stable Core 𝕊 = (L[S],S) was introduced. It was shown that V is generic over 𝕊 (for 𝕊-definable dense classes), each V-definable club contains an 𝕊-definable club, and the same holds with 𝕊 replaced by (HOD,S), where HOD denotes Gödel's inner model of hereditarily ordinal-definable sets. In the present article we extend this to models of class theory by introducing the V-definable Enriched Stable Core 𝕊* = (L[S*],S*). As an application...

Around stable forking

Byunghan Kim, A. Pillay (2001)

Fundamenta Mathematicae

Similarity:

We discuss various conjectures and problems around the issue of when and whether stable formulas are responsible for forking in simple theories. We prove that if the simple theory T has strong stable forking then any complete type is a nonforking extension of a complete type which is axiomatized by instances of stable formulas. We also give another treatment of the first author's result which identifies canonical bases in supersimple theories.

Definable quantifiers in second order arithmetic and elementary extensions of ω-models

Wojciech Guzicki

Similarity:

CONTENTS0. Introduction and terminology..............................................................51. Quantifiers and elementary extensions..............................................82. Elementary extensions of countable models of set theory................153. Interpretations of set theory in extensions of A₂...............................214. Definable quantifiers in models of A₂...............................................325. Elementary generic extensions........................................................40References..........................................................................................50 ...

On the number of countable models of stable theories

Predrag Tanović (2001)

Fundamenta Mathematicae

Similarity:

We prove: Theorem. If T is a countable, complete, stable, first-order theory having an infinite set of constants with different interpretations, then I(T,ℵ₀) ≥ ℵ₀.

A Note on the Uniqueness of Stable Marriage Matching

Ewa Drgas-Burchardt (2013)

Discussiones Mathematicae Graph Theory

Similarity:

In this note we present some sufficient conditions for the uniqueness of a stable matching in the Gale-Shapley marriage classical model of even size. We also state the result on the existence of exactly two stable matchings in the marriage problem of odd size with the same conditions.