"Mathematics is the Logic of the Infinite": Zermelo's Project of Infinitary Logic

Jerzy Pogonowski
2021 Studies in Logic, Grammar and Rhetoric  
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
doi:10.2478/slgr-2021-0042 fatcat:nnowhogl3bhklm234xa7dion7u