scholarly journals Forcing with matrices of countable elementary submodels

2017 ◽  
Vol 145 (5) ◽  
pp. 2211-2222
Author(s):  
Borisa Kuzeljevic ◽  
Stevo Todorcevic
Keyword(s):  
Elementary Submodels

scholarly journals The topology of elementary submodels

1998 ◽  
Vol 82 (1-3) ◽  
pp. 239-266 ◽  
Author(s):  
Lúcia R. Junqueira ◽  
Franklin D. Tall
Keyword(s):  
Elementary Submodels

scholarly journals Main gap for locally saturated elementary submodels of a homogeneous structure

2001 ◽  
Vol 66 (3) ◽  
pp. 1286-1302 ◽  
Author(s):  
Tapani Hyttinen ◽  
Saharon Shelah
Keyword(s):  
Homogeneous Structure ◽  
Elementary Submodels ◽  
Saturated Models ◽  
Gap Theorem

AbstractWe prove a main gap theorem for locally saturated submodels of a homogeneous structure. We also study the number of locally saturated models, which are not elementarily embeddable into each other.

scholarly journals Compact spaces, elementary submodels, and the countable chain condition

2006 ◽  
Vol 144 (1-3) ◽  
pp. 107-116 ◽  
Author(s):  
Lúcia R. Junqueira ◽  
Paul Larson ◽  
Franklin D. Tall
Keyword(s):  
Chain Condition ◽  
Compact Spaces ◽  
Elementary Submodels ◽  
Countable Chain Condition ◽  
Countable Chain

Unique decomposition in classifiable theories

2002 ◽  
Vol 67 (1) ◽  
pp. 61-68
Author(s):  
Bradd Hart ◽  
Ehud Hrushovski ◽  
Michael C. Laskowski
Keyword(s):  
Stability Theory ◽  
Saturated Model ◽  
Prime Model ◽  
Order Property ◽  
Elementary Submodels ◽  
Saturated Models ◽  
Unique Decomposition ◽  
Elementary Submodel

By a classifiable theory we shall mean a theory which is superstable, without the dimensional order property, which has prime models over pairs. In order to define what we mean by unique decomposition, we remind the reader of several definitions and results. We adopt the usual conventions of stability theory and work inside a large saturated model of a fixed classifiable theory T; for instance, if we write M ⊆ N for models of T, M and N we are thinking of these models as elementary submodels of this fixed saturated models; so, in particular, M is an elementary submodel of N. Although the results will not depend on it, we will assume that T is countable to ease notation.We do adopt one piece of notation which is not completely standard: if T is classifiable, M0 ⊆ Mi for i = 1, 2 are models of T and M1 is independent from M2 over M0 then we write M1M2 for the prime model over M1 ∪ M2.

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