A model and its subset: the uncountable case

Ludomir Newelski
1995 Annals of Pure and Applied Logic  
Assume Q is a definable subset of a model of T. We define a notion of Q-isolated type, generalizing an earlier definition for countable Q. This notion is absolute. For superstable T, we give some sufficient conditions for the existence of Q-atomic models. We apply this to prove some results on weak categoricity over a predicate. ' Research supported by KBN grant 2-l 103-91-01. E-mail: newelski@impan.impan.gov.pl 0168-0072/95/$09.50 G 1995-Elsevier Science B.V. All rights reserved SSDI
more » ... 94)EOOOl6-V (b) Ifu -b then for every c E A there is a d E B and for every d E B there is a c E A such that UC -bd. The classical theorem of Karp [6] says that two models M, N are L"-equivalent iff there is a back-and-forth relation -between M and N. So we say that A,B are L" -equivalent (A =, B) iff there is a back-and-forth relation between A and B. We define also a localized version of L"-equivalence: for c,d c 6 let (A;c) E, (B;d) iff there is a back-and-forth relation -between A and B such that ab implies UC = bd.
doi:10.1016/0168-0072(95)91363-f fatcat:fo75nzoqsfdq3hkbbpwnjl5u3u