A fundamental dichotomy for definably complete expansions of ordered fields

Antongiulio Fornasiero, Philipp Hieronymi

Research output: Contribution to journalArticlepeer-review

Abstract

An expansion of a definably complete field either defines a discrete subring, or the image of every definable discrete set under every definable map is nowhere dense. As an application we show a definable version of Lebesgue’s differentiation theorem.

Original languageEnglish (US)
Pages (from-to)1091-1115
Number of pages25
JournalJournal of Symbolic Logic
Volume80
Issue number4
DOIs
StatePublished - Dec 22 2015

Keywords

  • Definably complete
  • Lebesgue’s differentiation theorem
  • Second-order arithmetic

ASJC Scopus subject areas

  • Philosophy
  • Logic

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