Decidability and ℵ0-categoricity of theories of partially ordered sets-Reference-Cited by-同舟云学术

Decidability and ℵ0-categoricity of theories of partially ordered sets

Published:1980-09 Issue:3 Volume:45 Page:585-611
ISSN:0022-4812
Container-title:Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

Schmerl James H.

Abstract

AbstractThis paper is primarily concerned with ℵ0-categoricity of theories of partially ordered sets. It contains some general conjectures, a collection of known results and some new theorems on ℵ0-categoricity. Among the latter are the following.Corollary 3.3. For every countable ℵ0-categorical

there is a linear order of A such that (, <) is ℵ0-categorical.

Corollary 6.7. Every ℵ0-categorical theory of a partially ordered set of finite width has a decidable theory.Theorem 7.7. Every ℵ0-categorical theory of reticles has a decidable theory.There is a section dealing just with decidability of partially ordered sets, the main result of this section beingTheorem 8.2. If (P, <) is a finite partially ordered set and KP is the class of partially ordered sets which do not embed (P, <), then Th(KP) is decidable iff KP contains only reticles.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

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