DOAJ Open Access 2023

The Cardinal Squaring Principle and an Alternative Axiomatization of NFU

Tin Adlešić Vedran Čačić

Abstrak

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.

Topik & Kata Kunci

Logic

Penulis (2)

Tin Adlešić

Vedran Čačić

Format Sitasi

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Adlešić, T., Čačić, V. (2023). The Cardinal Squaring Principle and an Alternative Axiomatization of NFU. https://doi.org/10.18778/0138-0680.2023.25

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Informasi Jurnal

Tahun Terbit: 2023
Sumber Database: DOAJ
DOI: 10.18778/0138-0680.2023.25
Akses: Open Access ✓