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Page 3576 of Mathematical Reviews Vol. , Issue 2001F
[page]

2001
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Mathematical Reviews
*

The paper under review presents an example of

*a**supersimple**nonlow**theory*and characterizes its independence relation. O. V. ... Carlo Toffalori (l-CAM-MP; Camerino) 20011:03066 03C45 Casanovas, Enrique (E-BARU-HS; Barcelona); Kim, Byunghan (1-MIT; Cambridge, MA)*A**supersimple**nonlow**theory*. (English summary) Notre Dame J. ...##
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On ω-categorical simple theories
[article]

2011
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arXiv
*
pre-print

In the present paper we shall prove that countable \omega-categorical simple CM-trivial

arXiv:1102.3631v2
fatcat:yel6d234gnfbhjag4q6b4jlqri
*theories*and countable \omega-categorical simple*theories*with strong stable forking are low. ... In addition, we observe that simple*theories*of bounded finite weight are low. ... However, Casanovas and Kim [5] proved the existence of*a**supersimple**nonlow**theory*. ...##
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Random graphs with a random bijection

2011
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Tsukuba Journal of Mathematics
*

We show that the

doi:10.21099/tkbjm/1311081455
fatcat:dsyxzdjtubhabk5t7tioxygm6m
*theory*of random graphs with*a*bijection between the binary Cartesian product of the universe and the universe has*a*model companion which is complete, simple, and unsupersimple. ... Then, ðCD 0 ; NÞ is*a*good pair. So identifying CD 0 and clðb 1*Á**Á**Á*b n Þ, we can embed N in M. Take any i < o. Because CD i is closed, by Lemma 4.1, tpðD i =CÞ ¼ tpðD 0 =CÞ. ... In [2] , Casanovas and Kim showed an example of*a**supersimple**nonlow**theory*. Their structure is divided into two sorts, the sort for points and the sort for sets. ...##
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Cardinal Characteristics of Models of Set Theory
[article]

2018
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arXiv
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pre-print

In particular, we give streamlined proofs of the existence of minimal unstable, unsimple and

arXiv:1811.05444v1
fatcat:4eagmxgjnff2bo67odhbfvmy5a
*nonlow**theories*in these orders, and we give*a*similar analysis of the hypergraph examples T_n, k of Hrushovski ... We also prove that if B is*a*complete Boolean algebra with the λ-c.c., then no nonprincipal ultrafilter on U λ^+-saturates any unsimple*theory*. ... -minimal*nonlow**theory*(seeing as it is not*supersimple*). ...##
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Page 112 of Mathematical Reviews Vol. , Issue Subject Index
[page]

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Mathematical Reviews
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*Supersimple*

*theories*. 2001j:03065 Casanovas, Enrique (with Kim, Byunghan)

*A*

*supersimple*

*nonlow*

*theory*. (English summary) 2001f:03066 Evans, David M. (with Wagner, Frank O.) ...

*A*. Primitively connected

*theories*. (Russian. ...

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Lovely pairs of models

2003
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Annals of Pure and Applied Logic
*

We introduce the notion of

doi:10.1016/s0168-0072(03)00018-6
fatcat:lwmoglsjsjhxvd25vewo5isucu
*a*lovely pair of models of*a*simple*theory*T , generalizing Poizat's "belles paires" of models of*a*stable*theory*and the third author's "generic pairs" of models of an SU -rank ... We characterize when*a*saturated model of the*theory*TP of lovely pairs is*a*lovely pair (that is when the notion of*a*lovely pair is "axiomatizable"), ÿnding an analog of the nonÿnite cover property for ... -categorical 1-based simple*theory*is*supersimple*of ÿnite SU -rank (in particular low). ...##
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On the existence of indiscernible trees

2012
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Annals of Pure and Applied Logic
*

Such

doi:10.1016/j.apal.2012.05.012
fatcat:3rnuetirajd2togfe42kqd2tdu
*a*set*A*is also called*a*tree in this paper. We study the indiscernibility of trees*A*in general settings and apply the obtained results to the study of unstable*theories*. ...*A*tree is by definition an ordered set (O , <) such that, for any*a*∈ O , the initial segment {b ∈ O : b <*a*} determined by*a*is*a*linearly ordered set. ... So it is natural to ask whether there is*a*simple*nonlow**theory*T such that D inp (x = x, ϕ(x, y)) < ω for any ϕ. We prove that there is no such*theory*. Proposition 36. ...##
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Page 951 of Mathematical Reviews Vol. , Issue Author Index
[page]

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Mathematical Reviews
*

(Shu Huang Xiang) 2001g:39061 39B52 (46B20, 47H99)
Kim, Byungdo see Kim, Byung-Do
Kim, Byunghan (with Casanovas, Enrique)

*A**supersimple**nonlow**theory*. (English summary) Notre Dame J. ... Proceedings of the 31st Symposium on Ring*Theory*and Representation*Theory*and Japan-Korea Ring*Theory*and Representation*Theory*Seminar (Osaka, 1998), 82-87, Shinshu Univ., Matsumoto, 1999. 16D25 Kim, ...##
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Page 274 of Mathematical Reviews Vol. , Issue Author Index
[page]

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Mathematical Reviews
*

*supersimple*

*nonlow*

*theory*. ... Troubetzkoy) 2001d:37031 37D20 (37A99, 37C85) Carvalho, Paula

*A*.

*A*. B. (with Musson, lan M.) Down-up algebras and their representa- tion

*theory*. (English summary) J. ...

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Some Applications of Set Theory to Model Theory

2019
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Bulletin of Symbolic Logic
*

Keisler's order is

doi:10.1017/bsl.2019.4
fatcat:pkb5kwre3zervovtxef3koexpu
*a*pre-order on complete countable*theories*T , measuring the saturation of ultrapowers of models of T . In Chapter 3, we present*a*self-contained survey on Keisler's order. ... We also investigate the model-theoretic properties detected by Keisler's order among the simple unstable*theories*. ... -minimal*nonlow**theory*T Cas . ...