The Cardinal Squaring Principle and an Alternative Axiomatization of NFU
In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (V...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Lodz University Press
2023-09-01
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| Series: | Bulletin of the Section of Logic |
| Subjects: | |
| Online Access: | https://czasopisma.uni.lodz.pl/bulletin/article/view/14771 |
| Summary: | In this paper, we rigorously prove the existence of type-level ordered pairs in Quine’s New Foundations with atoms, augmented by the axiom of infinity and the axiom of choice (NFU + Inf + AC). The proof uses the cardinal squaring principle; more precisely, its instance for the (infinite) universe (VCSP), which is a theorem of NFU + Inf + AC. Therefore, we have a justification for proposing a new axiomatic extension of NFU, in order to obtain type-level ordered pairs almost from the beginning. This axiomatic extension is NFU + Inf + AC + VCSP, which is equivalent to NFU + Inf + AC, but easier to reason about. |
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| ISSN: | 0138-0680 2449-836X |