Theories of linear order

Matatyahu Rubin

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33 Scopus citations

Abstract

Let T be a complete theory of linear order; the language of T may contain a finite or a countable set of unary predicates. We prove the following results. (i) The number of nonisomorphic countable models of T is either finite or 2ω. (ii) If the language of T is finite then the number of nonisomorphic countable models of T is either 1 or 2ω. (iii) If S 1(T) is countable then so is S n(T) for every n. (iv) In case S 1(T) is countable we find a relation between the Cantor Bendixon rank of S 1(T) and the Cantor Bendixon rank of S n(T). (v) We define a class of models L, and show that S 1(T) is finite iff the models of T belong to L. We conclude that if S 1(T) is finite then T is finitely axiomatizable. (vi) We prove some theorems concerning the existence and the structure of saturated models.

Original languageEnglish
Pages (from-to)392-443
Number of pages52
JournalIsrael Journal of Mathematics
Volume17
Issue number4
DOIs
StatePublished - 1 Mar 1974
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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