Zermelo 1935

pp. 582-599

in: Ernst Zermelo, Set theory, miscellanea / Mengenlehre, varia, Berlin, Springer, 2010

Abstract

The following considerations elaborate ideas whose preliminary outlines I surveyed in September 1932 at the meeting of mathematicians in Bad Elster (see Zermelo 1932a). They essentially rest on the concept of the "founding relations" of which I already made use in 1930 in my paper on "boundary numbers and domains of sets" (Zermelo 1930a) in the special case of the ε-relation (the insertion of an element into a set). I therefore begin with a general characterization of this concept, which, in a certain sense, extends Cantor's "well-ordering", and then turn to its application to the syllogistic of propositional systems.