A Classical Modal Theory of Lawless Sequences

Ethan BRAUER*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

Abstract

Free choice sequences play a key role in the intuitionistic theory of the continuum and especially in the theorems of intuitionistic analysis that conflict with classical analysis, leading many classical mathematicians to reject the concept of a free choice sequence. By treating free choice sequences as potentially infinite objects, however, they can be comfortably situated alongside classical analysis, allowing a rapprochement of these two mathematical traditions. Building on recent work on the modal analysis of potential infinity, I formulate a modal theory of the free choice sequences known as lawless sequences. Intrinsically well-motivated axioms for lawless sequences are added to a background theory of classical second-order arithmetic, leading to a theory I call MCLS. This theory interprets the standard intuitionistic theory of lawless sequences and is conservative over the classical background theory.
Original languageEnglish
Pages (from-to)406-452
Number of pages47
JournalBulletin of Symbolic Logic
Volume29
Issue number3
Early online date9 Mar 2023
DOIs
Publication statusPublished - 9 Sept 2023

Bibliographical note

Publisher Copyright:
© The Author(s), 2023.

Keywords

  • Brouwer
  • free choice sequences
  • intuitionism
  • intuitionistic analysis
  • potential infinity
  • potentialism

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