- Tytuł:
- The Cardinal Squaring Principle and an Alternative Axiomatization of NFU
- Autorzy:
-
Adlešić, Tin
Čačić, Vedran - Powiązania:
- https://bibliotekanauki.pl/articles/43182311.pdf
- Data publikacji:
- 2023
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
Quine's New Foundations
cardinal multiplication
axiomatization - Opis:
- 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.
- Źródło:
-
Bulletin of the Section of Logic; 2023, 52, 4; 551-581
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł