The Cardinal Squaring Principle and an Alternative Axiomatization of NFU
| dc.contributor.author | Adlešić, Tin | |
| dc.contributor.author | Čačić, Vedran | |
| dc.date.accessioned | 2024-01-04T12:38:40Z | |
| dc.date.available | 2024-01-04T12:38:40Z | |
| dc.date.issued | 2023-09-28 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/49162 | |
| dc.description.abstract | 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. | en |
| dc.language.iso | en | |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl |
| dc.relation.ispartofseries | Bulletin of the Section of Logic;4 | en |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | Quine's New Foundations | en |
| dc.subject | cardinal multiplication | en |
| dc.subject | axiomatization | en |
| dc.title | The Cardinal Squaring Principle and an Alternative Axiomatization of NFU | en |
| dc.type | Other | |
| dc.page.number | 551-581 | |
| dc.contributor.authorAffiliation | Adlešić, Tin - University of Zagreb, Faculty of Teacher education | en |
| dc.contributor.authorAffiliation | Čačić, Vedran - University of Zagreb, Faculty of Science | en |
| dc.identifier.eissn | 2449-836X | |
| dc.references | T. Adlešić, V. Čačić, A Modern Rigorous Approach to Stratification in NF/NFU, Logica Universalis, vol. 16(3) (2022), pp. 451–468, DOI: https://doi.org/10.1007/s11787-022-00310-y | en |
| dc.references | H. B. Enderton, Elements of set theory, Academic press (1977), DOI: https://doi.org/https://doi.org/10.1016/C2009-0-22079-4 | en |
| dc.references | H. B. Enderton, A Mathematical Introduction to Logic, Academic Press (2001). | en |
| dc.references | M. J. Gabbay, Consistency of Quine’s New Foundations (2014), DOI: https://doi.org/10.48550/ARXIV.1406.4060 | en |
| dc.references | M. R. Holmes, Systems of combinatory logic related to Quine’s ‘New Foundations’, Annals of Pure and Applied Logic, vol. 53(2) (1991), pp. 103–133, DOI: https://doi.org/10.1016/0168-0072(91)90052-N | en |
| dc.references | M. R. Holmes, The set-theoretical program of Quine succeeded, but nobody noticed, Modern Logic, (1994). | en |
| dc.references | M. R. Holmes, Elementary set theory with a universal set, https://randall-holmes.github.io/head.pdf (1998). | en |
| dc.references | M. R. Holmes, A new pass at the NF consistency proof, https://randall-holmes.github.io/Nfproof/newattempt.pdf (2020). | en |
| dc.references | M. R. Holmes, Proof, Sets, and Logic, https://randall-holmes.github.io/proofsetslogic.pdf (2021). | en |
| dc.references | M. R. Holmes, F. E. Forster, T. Libert, Alternative Set Theories., Sets and extensions in the twentieth century, vol. 6 (2012), pp. 559–632. | en |
| dc.references | R. B. Jensen, On the consistency of a slight (?) modification of Quine’s New Foundations, [in:] J. Hintikka (ed.), Words and objections: Essays on the Work of W. V. Quine, Springer (1969), pp. 278–291. | en |
| dc.references | W. V. Quine, New foundations for mathematical logic, The American mathematical monthly, (1937), DOI: https://doi.org/10.2307/2267377 | en |
| dc.references | J. B. Rosser, Logic for mathematicians, Dover Publications (2008), DOI: https://doi.org/10.2307/2273431 | en |
| dc.references | G. Wagemakers, New Foundations—A survey of Quine’s set theory, Master’s thesis, Instituut voor Tall, Logica en Informatie Publication Series, X-89-02 (1989). | en |
| dc.contributor.authorEmail | Adlešić, Tin - tin.adlesic@ufzg.hr | |
| dc.contributor.authorEmail | Čačić, Vedran - veky@math.hr | |
| dc.identifier.doi | 10.18778/0138-0680.2023.25 | |
| dc.relation.volume | 52 |
Pliki tej pozycji
Pozycja umieszczona jest w następujących kolekcjach
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako https://creativecommons.org/licenses/by-nc-nd/4.0