countable models
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2020 ◽  
Vol 66 (2) ◽  
pp. 182-189
Author(s):  
John Clemens ◽  
Samuel Coskey ◽  
Samuel Dworetzky

2020 ◽  
Vol 171 (3) ◽  
pp. 102765
Author(s):  
Slavko Moconja ◽  
Predrag Tanović
Keyword(s):  

2020 ◽  
Vol 11 (3) ◽  
pp. 66-78
Author(s):  
Beibut Kulpeshov ◽  
◽  
Sergey Sudoplatov ◽  
◽  
◽  
...  
Keyword(s):  

2019 ◽  
Vol 84 (3) ◽  
pp. 1168-1175
Author(s):  
BYUNGHAN KIM

AbstractIn this article, we prove that if a countable non-${\aleph _0}$-categorical NSOP1 theory with nonforking existence has finitely many countable models, then there is a finite tuple whose own preweight is ω. This result is an extension of a theorem of the author on any supersimple theory.


2019 ◽  
Vol 84 (3) ◽  
pp. 1007-1019
Author(s):  
DANUL K. GUNATILLEKA

AbstractWe continue the study of the theories of Baldwin–Shi hypergraphs from [5]. Restricting our attention to when the rank δ is rational valued, we show that each countable model of the theory of a given Baldwin–Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class used in the construction. We introduce a notion of dimension for a model and show that there is a an elementary chain $\left\{ {\mathfrak{M}_\beta :\beta \leqslant \omega } \right\}$ of countable models of the theory of a fixed Baldwin–Shi hypergraph with $\mathfrak{M}_\beta \preccurlyeq \mathfrak{M}_\gamma $ if and only if the dimension of $\mathfrak{M}_\beta $ is at most the dimension of $\mathfrak{M}_\gamma $ and that each countable model is isomorphic to some $\mathfrak{M}_\beta $. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on a large body of work, we use these structures to give an example of a pseudofinite, ω-stable theory with a nonlocally modular regular type, answering a question of Pillay in [11].


2019 ◽  
Vol 84 (02) ◽  
pp. 589-620
Author(s):  
KAMERYN J. WILLIAMS

AbstractIn this article I investigate the phenomenon of minimum and minimal models of second-order set theories, focusing on Kelley–Morse set theory KM, Gödel–Bernays set theory GB, and GB augmented with the principle of Elementary Transfinite Recursion. The main results are the following. (1) A countable model of ZFC has a minimum GBC-realization if and only if it admits a parametrically definable global well order. (2) Countable models of GBC admit minimal extensions with the same sets. (3) There is no minimum transitive model of KM. (4) There is a minimum β-model of GB+ETR. The main question left unanswered by this article is whether there is a minimum transitive model of GB+ETR.


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