Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-19T23:34:24.395Z Has data issue: false hasContentIssue false

DECIDABLE MODELS OF ω-STABLE THEORIES

Published online by Cambridge University Press:  17 April 2014

URI ANDREWS*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN, MADISON 480 LINCOLN DR., MADISON, WI 53706-1388, USAE-mail: andrews@math.wisc.edu

Abstract

We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T, every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many countable models as those which realize only recursive types.

Type
Articles
Copyright
Copyright © Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bouscaren, Elisabeth, Martin’s conjecture for ω-stable theories. Israel Journal of Mathematics, vol. 49 (1984), no. 1–3, pp. 1525.Google Scholar
Buechler, Steven, Resplendency and recursive definability in ω-stable theories. Israel Journal of Mathematics, vol. 49 (1984), no. 1–3, pp. 2633.Google Scholar
Buechler, Steven, Vaught’s conjecture for superstable theories of finite rank. Annals of Pure and Applied Logic, vol. 155 (2008), no. 3, pp. 135172.Google Scholar
Goncharov, Sergei and Nurtazin, Abyz T., Constructive models of complete decidable theories. Algebra and Logic, vol. 12 (1973), pp. 6777.Google Scholar
Harrington, Leo, Recursively presentable prime models, this Journal, vol. 39 (1974), pp. 305309.Google Scholar
Khisamiev, Nazif G., Strongly constructive models of a decidable theory. Izvestiya Akademiya Nauk Kazakhstan SSR Seriya Fiziko-Matematicheskaya, (1974), no. 1, pp. 8384, 94.Google Scholar
Millar, Terrence, Omitting types, type spectrums, and decidability, this Journal, vol. 48 (1983), no. 1, pp. 171181.Google Scholar
Millar, Terrence, Decidability and the number of countable models. Annals of Pure and Applied Logic, vol. 27 (1984), no. 2, pp. 137153.Google Scholar
Millar, Terrence, Prime models and almost decidability, this Journal, vol. 51 (1986), no. 2, pp. 412420.Google Scholar
Shelah, S., Harrington, L., and Makkai, M., A proof of Vaught’s conjecture for ω-stable theories. Israel Journal of Mathematics, vol. 49 (1984), no. 1–3, pp. 259280.Google Scholar