Description

• Title:
  The Cardinal Squaring Principle and an Alternative Axiomatization of NFU
• Creator:
  Adlešić, Tin;
  Čačić, Vedran
• Contributor:
  Adlešić, Tin - University of Zagreb, Faculty of Teacher education;
  Čačić, Vedran - University of Zagreb, Faculty of Science;
  Adlešić, Tin - tin.adlesic@ufzg.hr;
  Čačić, Vedran - veky@math.hr
• Description:
  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.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2024.01.04;
  2023.09.28
• Type:
  Other
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;4;
  52
• Subject:
  Quine's New Foundations;
  cardinal multiplication;
  axiomatization
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/49162 ;
  2449-836X;
  10.18778/0138-0680.2023.25
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  other