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Einige Bemerkungen zu der Abhandlung von E.~Zermelo: ӆber die Definitheit in der Axiomatik'

In Selected Works in Logic. Universitetsforlaget. pp. 276--9 (1930)

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  1. The Mathematical Development of Set Theory From Cantor to Cohen.Akihiro Kanamori - 1996 - Bulletin of Symbolic Logic 2 (1):1-71.
    Set theory is an autonomous and sophisticated field of mathematics, enormously successful not only at its continuing development of its historical heritage but also at analyzing mathematical propositions cast in set-theoretic terms and gauging their consistency strength. But set theory is also distinguished by having begun intertwined with pronounced metaphysical attitudes, and these have even been regarded as crucial by some of its great developers. This has encouraged the exaggeration of crises in foundations and of metaphysical doctrines in general. However, (...)
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  • Zermelo: Definiteness and the Universe of Definable Sets.Heinz-Dieter Ebbinghaus - 2003 - History and Philosophy of Logic 24 (3):197-219.
    Using hitherto unpublished manuscripts from the Zermelo Nachlass, I describe the development of the notion of definiteness and the discussion about it, giving a conclusive picture of Zermelo's thoughts up to the late thirties. As it turns out, Zermelo's considerations about definiteness are intimately related to his concept of a Cantorian universe of categorically definable sets that may be considered an inner model of set theory in an ideationally given universe of classes.
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  • Reflections on Skolem's Relativity of Set-Theoretical Concepts.Ignagio Jane - 2001 - Philosophia Mathematica 9 (2):129-153.
    In this paper an attempt is made to present Skolem's argument, for the relativity of some set-theoretical notions as a sensible one. Skolem's critique of set theory is seen as part of a larger argument to the effect that no conclusive evidence has been given for the existence of uncountable sets. Some replies to Skolem are discussed and are shown not to affect Skolem's position, since they all presuppose the existence of uncountable sets. The paper ends with an assessment of (...)
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