Author:
Harnik Victor,Makkai Michael
Abstract
AbstractWe use a fundamental theorem of Vaught, called the covering theorem in [V] (cf. theorem 0.1 below) as well as a generalization of it (cf. Theorem 0.1* below) to derive several known and a few new results related to the logic . Among others, we prove that if every countable model in a PCφ1ω class has only countably many automorphisms, then the class has either ≤ℵ0 or exactly nonisomorphic countable members (cf. Theorem 4.3*) and that the class of countable saturated structures of a sufficiently large countable similarity type is not among countable structures (cf. Theorem 5.2). We also give a simple proof of the Lachlan-Sacks theorem on bounds of Morley ranks (§7).
Publisher
Cambridge University Press (CUP)
Reference27 articles.
1. A theorem on permutations in models
2. Motohashi N. , A new theorem on definability, preprint; also, Dissertation, University of Tokyo, 1971.
3. Svenonius sentences and Lindström's theory on preservation theorems
4. Perfect subsets of definable sets of real numbers
5. Sacks G. E. , On the number of countable models (to appear).
Cited by
5 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献