Zermelo’s Axiom and Axiomatization in Transition (1908–1918)

Author:

Moore Gregory H.

Publisher

Springer New York

Reference119 articles.

1. Letter of 7 November 1903 to Frege, in Frege 1980, 51–52.

2. Zermelo 1908, 108, 117. For a given set M and a given choice function f on the family of all non-empty subsets of M, T is a θ-chain if (1) T is a set of subsets of M; (2) M is in T; (3) if A is in T, then A - {f(A)} is in T; (4) if S is a subset of T, then ⋂ S is in T.

3. Zermelo corresponded with Jourdain in 1907, but apparently their letters focused on a generalization of König’s theorem (2.1.2); see Jourdain 1908, 512.

4. DMV 14 (1905), 61.

5. This was a jibe at Peano’s admiration for the Scholastics.

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