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arXiv · 2407.18969

Relative consistency of a finite nonclassical theory incorporating ZF and category theory with ZF

Marcoen J. T. F. Cabbolet·Adrian R. D. Mathias
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Abstract

Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker than ZF, that is finitely axiomatized, and that does not have a countable model (if it has a model at all, that is). Here we prove that T is relatively consistent with ZF. We conclude that this is an important step towards showing that T is an advancement in the foundations of mathematics.

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Marcoen J. T. F. Cabbolet, Adrian R. D. Mathias. 2024-07-21. Relative consistency of a finite nonclassical theory incorporating ZF and category theory with ZF. https://arxiv.org/abs/2407.18969

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