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Countable models of weakly quasi-o-minimal theories II

Slavko Moconja, Predrag Tanović

Abstract

We confirm Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.

Countable models of weakly quasi-o-minimal theories II

Abstract

We confirm Martin's conjecture for a broad subclass of weakly quasi-o-minimal theories.
Paper Structure (14 sections, 39 theorems, 38 equations)

This paper contains 14 sections, 39 theorems, 38 equations.

Table of Contents

  1. Introduction and preliminaries
  2. Preliminaries
  3. $\mathbf p$-semiintervals
  4. Simplicity of $\mathbf p$-semiintervals
  5. Simplicity of semiintervals and binary forking dependence
  6. Existence of shifts vs simplicity of semiintervals
  7. Condition (R)
  8. Convex types, definabilty and triviality
  9. $p$-large sets
  10. Convex weakly o-minimal types
  11. Definability vs triviality of convex types
  12. Martin's conjecture
  13. Proof of Theorem \ref{['Theorem_AAC']}
  14. Concluding remarks

Key Result

Theorem 1

Let $T$ be a countable, weakly quasi-o-minimal theory. Suppose that at least one of the following two conditions holds. Then $I(T,\aleph_0)=2^{\aleph_0}$.

Theorems & Definitions (103)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Definition 2.1
  • Remark 2.2
  • Lemma 2.3
  • proof
  • Remark 2.4
  • Lemma 2.5
  • proof
  • ...and 93 more