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 language | English |
|---|---|
| Pages (from-to) | 406-452 |
| Number of pages | 47 |
| Journal | Bulletin of Symbolic Logic |
| Volume | 29 |
| Issue number | 3 |
| Early online date | 9 Mar 2023 |
| DOIs | |
| Publication status | Published - 9 Sept 2023 |
Bibliographical note
Publisher Copyright:© The Author(s), 2023.
Funding
This research was supported by the Hong Kong Research Grants Council grant PDFS2021-3H05.
Keywords
- Brouwer
- free choice sequences
- intuitionism
- intuitionistic analysis
- potential infinity
- potentialism