Class Theory in HYPE

doi:10.1215/00294527-2025-0009

2025-11-01

PRE

Maria Beatrice Buonaguidi *

Carlo Nicolai

DOI：10.1215/00294527-2025-0009

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This paper studies class theory over the logic HYPE recently introduced by Hannes Leitgeb. We formulate suitable abstraction principles and show their consistency by displaying a class of fixed-point (term) models. By adapting a classical result by Brady, we show their inconsistency with standard extensionality principles, as well as the incompatibility of our semantics with weak extensionality principles introduced in the literature. We then formulate our version of weak extensionality (appropriate to the behavior of the conditional in HYPE) and show its consistency with one of the abstraction principles previously introduced. We conclude with observations and examples supporting the claim that, although arithmetical axioms over HYPE are as strong as classical arithmetical axioms, the behavior of classes over HYPE is akin to the one displayed by classes in other nonclassical class theories.

Keyword:

Subject Primary nonclassical logics

abstraction

extensionality