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

2001 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.  ... 

On ω-categorical simple theories [article]

Daniel Palacin
2011 arXiv   pre-print
In the present paper we shall prove that countable \omega-categorical simple CM-trivial 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.  ... 
arXiv:1102.3631v2 fatcat:yel6d234gnfbhjag4q6b4jlqri

Random graphs with a random bijection

Yuki Anbo
2011 Tsukuba Journal of Mathematics  
We show that the 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.  ... 
doi:10.21099/tkbjm/1311081455 fatcat:dsyxzdjtubhabk5t7tioxygm6m

Cardinal Characteristics of Models of Set Theory [article]

Douglas Ulrich
2018 arXiv   pre-print
In particular, we give streamlined proofs of the existence of minimal unstable, unsimple and 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).  ... 
arXiv:1811.05444v1 fatcat:4eagmxgjnff2bo67odhbfvmy5a

Page 112 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
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.  ... 

Lovely pairs of models

Itay Ben-Yaacov, Anand Pillay, Evgueni Vassiliev
2003 Annals of Pure and Applied Logic  
We introduce the notion of 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).  ... 
doi:10.1016/s0168-0072(03)00018-6 fatcat:lwmoglsjsjhxvd25vewo5isucu

On the existence of indiscernible trees

Kota Takeuchi, Akito Tsuboi
2012 Annals of Pure and Applied Logic  
Such 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.  ... 
doi:10.1016/j.apal.2012.05.012 fatcat:3rnuetirajd2togfe42kqd2tdu

Page 951 of Mathematical Reviews Vol. , Issue Author Index [page]

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,  ... 

Page 274 of Mathematical Reviews Vol. , Issue Author Index [page]

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.  ... 

Some Applications of Set Theory to Model Theory

Douglas Ulrich
2019 Bulletin of Symbolic Logic  
Keisler's order is 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 .  ... 
doi:10.1017/bsl.2019.4 fatcat:pkb5kwre3zervovtxef3koexpu