<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.<sup>1</sup></p>
</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

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

Department of Logic and Cognitive Science

Studies in Logic, Grammar and Rhetoric

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

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

Published Online: Dec 30, 2021

Page range: 673 - 708

DOI: https://doi.org/10.2478/slgr-2021-0042

Keywords
infinitary logic, axiomatic set theory, extremal axiom

© 2021 Jerzy Pogonowski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Published Online: Dec 30, 2021

Page range: 673 - 708

DOI: https://doi.org/10.2478/slgr-2021-0042

Keywordsinfinitary logic, axiomatic set theory, extremal axiom

© 2021 Jerzy Pogonowski, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
infinitary logic, axiomatic set theory, extremal axiom