Annals of Pure and Applied Logic 171 (3):102765 (2020)

We introduce the notions of stationarily ordered types and theories; the latter generalizes weak o-minimality and the former is a relaxed version of weak o-minimality localized at the locus of a single type. We show that forking, as a binary relation on elements realizing stationarily ordered types, is an equivalence relation and that each stationarily ordered type in a model determines some order-type as an invariant of the model. We study weak and forking non-orthogonality of stationarily ordered types, show that they are equivalence relations and prove that invariants of non-orthogonal types are closely related. The techniques developed are applied to prove that in the case of a binary, stationarily ordered theory with fewer than countable models, the isomorphism type of a countable model is determined by a certain sequence of invariants of the model. In particular, we confirm Vaught's conjecture for binary, stationarily ordered theories.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2019.102765
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 50,241
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Types Directed by Constants.Predrag Tanović - 2010 - Annals of Pure and Applied Logic 161 (7):944-955.
Theories with a Finite Number of Countable Models.Robert E. Woodrow - 1978 - Journal of Symbolic Logic 43 (3):442-455.
Simple Groups and the Number of Countable Models.Predrag Tanović - 2013 - Archive for Mathematical Logic 52 (7-8):779-791.
Order Types of Ordinals in Models of Set Theory.John E. Hutchinson - 1976 - Journal of Symbolic Logic 41 (2):489-502.
Theories with Constants and Three Countable Models.Predrag Tanović - 2007 - Archive for Mathematical Logic 46 (5-6):517-527.
A Decidable Ehrenfeucht Theory with Exactly Two Hyperarithmetic Models.Robert C. Reed - 1991 - Annals of Pure and Applied Logic 53 (2):135-168.
A Note on Countable Models of 1-Based Theories.Predrag Tanovic - 2002 - Archive for Mathematical Logic 41 (7):669-671.
Non-Isolated Types in Stable Theories.Predrag Tanović - 2007 - Annals of Pure and Applied Logic 145 (1):1-15.
Unions and the Axiom of Choice.Omar de la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean Rubin - 2008 - Mathematical Logic Quarterly 54 (6):652-665.
On Constants and the Strict Order Property.Predrag Tanović - 2005 - Archive for Mathematical Logic 45 (4):423-430.


Added to PP index

Total views
13 ( #677,824 of 2,325,377 )

Recent downloads (6 months)
2 ( #451,872 of 2,325,377 )

How can I increase my downloads?


My notes