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.

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.

scholarly journals Localising the smallest stiffness and its direction of a homogeneous structure by spectral and optimisation approaches

2021 ◽  
Vol 232 ◽  
pp. 111842
Author(s):  
Petr Henyš ◽  
Danas Sutula ◽  
Jiří Kopal ◽  
Michal Kuchař ◽  
Lukáš Čapek
Keyword(s):  
Homogeneous Structure

Saturated models

1998 ◽  
Vol 43 (7) ◽  
pp. 562-564
Author(s):  
Guolong Chen
Keyword(s):  
Saturated Models

Automorphism groups of arithmetically saturated models

2006 ◽  
Vol 71 (1) ◽  
pp. 203-216 ◽  
Author(s):  
Ermek S. Nurkhaidarov
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Open Subgroup ◽  
Peano Arithmetic ◽  
Standard System ◽  
Permutation Groups ◽  
Saturated Model ◽  
Saturated Models ◽  
Homogeneous Set ◽  
Image Position

In this paper we study the automorphism groups of countable arithmetically saturated models of Peano Arithmetic. The automorphism groups of such structures form a rich class of permutation groups. When studying the automorphism group of a model, one is interested to what extent a model is recoverable from its automorphism group. Kossak-Schmerl [12] show that if M is a countable, arithmetically saturated model of Peano Arithmetic, then Aut(M) codes SSy(M). Using that result they prove:Let M1. M2 be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1) ≅ Aut(M2). Then SSy(M1) = SSy(M2).We show that if M is a countable arithmetically saturated of Peano Arithmetic, then Aut(M) can recognize if some maximal open subgroup is a stabilizer of a nonstandard element, which is smaller than any nonstandard definable element. That fact is used to show the main theorem:Let M1, M2be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1) ≅ Aut(M2). Then for every n < ωHere RT2n is Infinite Ramsey's Theorem stating that every 2-coloring of [ω]n has an infinite homogeneous set. Theorem 0.2 shows that for models of a false arithmetic the converse of Kossak-Schmerl Theorem 0.1 is not true. Using the results of Reverse Mathematics we obtain the following corollary:There exist four countable arithmetically saturated models of Peano Arithmetic such that they have the same standard system but their automorphism groups are pairwise non-isomorphic.

Containerless processing for preparation of akermanite bioceramic spheres with homogeneous structure, tailored bioactivity and degradation

2013 ◽  
Vol 1 (7) ◽  
pp. 1019-1026 ◽  
Author(s):  
Chengtie Wu ◽  
Minghui Zhang ◽  
Dong Zhai ◽  
Jianding Yu ◽  
Yan Liu ◽  
...  
Keyword(s):  
Homogeneous Structure ◽  
Containerless Processing

A Gap Theorem for Differentially Algebraic Power Series

Number Theory ◽  
1991 ◽  
pp. 211-214
Author(s):  
Leonard Lipshitz ◽  
Lee A. Rubel
Keyword(s):  
Power Series ◽  
Gap Theorem ◽  
Algebraic Power Series

scholarly journals Normal forms on contracting foliations: smoothness and homogeneous structure

2016 ◽  
Vol 183 (1) ◽  
pp. 181-194 ◽  
Author(s):  
Boris Kalinin ◽  
Victoria Sadovskaya
Keyword(s):  
Normal Forms ◽  
Homogeneous Structure
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