Gradualist descriptionalist set theory

David Simmons

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arXiv · 2603.27077

Gradualist descriptionalist set theory

David Simmons

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Abstract

We introduce a formal language GDST (gradualist descriptionalist set theory) with a family of interpretations indexed by ordinals, as well as a sublanguage NMID (the language of not necessarily monotonic inductive definitions), and show that the assertion that all propositions in NMID have well-defined truth values is equivalent to the existence for each $k \in \mathbb N$ of a sequence of ordinals $\eta_0 < . . . < \eta_k$ such that for each $i < k$, $\eta_i$ is $\eta_{i+1}$-reflecting, a notion we introduce which implies being $\Pi_n$-reflecting for all $n \in \mathbb N$ (and in particular being admissible and recursively Mahlo).

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BibTeX RIS

David Simmons. 2026-03-28. Gradualist descriptionalist set theory. https://arxiv.org/abs/2603.27077

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