Zermelo: a Well Founded Antiskolemism

Zermelo had in mind here his works listed below. They concern a foundational program formulated by him with special emphasis put on the infinitary (though always well founded) nature of mathematical proof. This idea is of course in sharp opposition to the (quite well established at that time) common uderstanding of the notion of finitary formal proof. Zermelo rejects what he himself calls Skolemism and the finitary prejudices: the views that set theory should be axiomatized in a first order language (which implies that quantification over propositional functions in the comprehension axiom would be out of question) and that mathematical theories in general should be codified solely in terms of finitary logic.