“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic-Reference-Cited by-同舟云学术

“Mathematics is the Logic of the Infinite”: Zermelo’s Project of Infinitary Logic

Published:2021-12-01 Issue:3 Volume:66 Page:673-708
ISSN:2199-6059
Container-title:Studies in Logic, Grammar and Rhetoric
language:en
Short-container-title:

Author:

Pogonowski Jerzy¹^ORCID

Affiliation:

1. Department of Logic and Cognitive Science , Adam Mickiewicz University in Poznań

Abstract

Abstract In this paper I discuss Ernst Zermelo’s ideas concerning the possibility of developing a system of infinitary logic that, in his opinion, should be suitable for mathematical inferences. The presentation of Zermelo’s ideas is accompanied with some remarks concerning the development of infinitary logic. I also stress the fact that the second axiomatization of set theory provided by Zermelo in 1930 involved the use of extremal axioms of a very specific sort.1

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/slgr-2021-0042

Reference114 articles.

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2. Barwise, J. 1974. Axioms for abstract model theory, Annals of Mathematical Logic 7, 221–265.

3. Barwise, J. 1975. Admissible Sets and Structures. An Approach to Definability Theory. Berlin Heidelberg New York: Springer Verlag.10.1007/978-3-662-11035-5_2

4. Barwise, J., Feferman, S. (Eds.) 1985. Model-theoretic Logics. New York Berlin Heidelberg Tokyo: Springer Verlag.

5. Batóg, T. 2000. Dwa paradygmaty matematyki. Studium z dziejów i filozofii mate-matyki. Poznań: Wydawnictwo Naukowe UAM.

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