PSEUDO-FINITE SETS, PSEUDO-O-MINIMALITY

Nadav Meir

Research output: Contribution to journalArticlepeer-review

Abstract

We give an example of two ordered structures M,N in the same language L with the same universe, the same order and admitting the same one-variable definable subsets such that M is a model of the common theory of o-minimal L-structures and N admits a definable, closed, bounded, and discrete subset and a definable injective self-mapping of that subset which is not surjective. This answers negatively two question by Schoutens; the first being whether there is an axiomatization of the common theory of o-minimal structures in a given language by conditions on one-variable definable sets alone. The second being whether definable completeness and type completeness imply the pigeonhole principle. It also partially answers a question by Fornasiero asking whether definable completeness of an expansion of a real closed field implies the pigeonhole principle.

Original languageEnglish
Pages (from-to)577-599
Number of pages23
JournalJournal of Symbolic Logic
Volume86
Issue number2
DOIs
StatePublished - 1 Jun 2021

Keywords

  • definably complete
  • o-minimalism
  • pigeonhole principle
  • pseudo-o-minimal
  • type complete

ASJC Scopus subject areas

  • Philosophy
  • Logic

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