Theories of linear order |
| |
Authors: | Matatyahu Rubin |
| |
Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
| |
Abstract: | LetT be a complete theory of linear order; the language ofT may contain a finite or a countable set of unary predicates. We prove the following results. (i) The number of nonisomorphic
countable models ofT is either finite or 2ω. (ii) If the language ofT is finite then the number of nonisomorphic countable models ofT is either 1 or 2ω. (iii) IfS
1(T) is countable then so isS
n(T) for everyn. (iv) In caseS
1(T) is countable we find a relation between the Cantor Bendixon rank ofS
1(T) and the Cantor Bendixon rank ofS
n(T). (v) We define a class of modelsL, and show thatS
1(T) is finite iff the models ofT belong toL. We conclude that ifS
1(T) is finite thenT is finitely axiomatizable. (vi) We prove some theorems concerning the existence and the structure of saturated models.
Most of the results in this paper appeared in the author’s Master of Science thesis which was prepared at the Hebrew University
under the supervision of Professor H. Gaifman. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|