Zermelo's Cantorian theory of systems of infinitely long propositions

Bulletin of Symbolic Logic 8 (4):478-515 (2002)
Abstract
In papers published between 1930 and 1935. Zermelo outlines a foundational program, with infinitary logic at its heart, that is intended to (1) secure axiomatic set theory as a foundation for arithmetic and analysis and (2) show that all mathematical propositions are decidable. Zermelo's theory of systems of infinitely long propositions may be termed "Cantorian" in that a logical distinction between open and closed domains plays a signal role. Well-foundedness and strong inaccessibility are used to systematically integrate highly transfinite concepts of demonstrability and existence. Zermelo incompleteness is then the analogue of the Problem of Proper Classes, and the resolution of these two anomalies is similarly analogous
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DOI 10.2178/bsl/1182353918
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References found in this work BETA
Zermelo, Reductionism, and the Philosophy of Mathematics.R. Gregory Taylor - 1993 - Notre Dame Journal of Formal Logic 34 (4):539--63.

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Zermelo: Boundary Numbers and Domains of Sets Continued.Heinz-Dieter Ebbinghaus - 2006 - History and Philosophy of Logic 27 (4):285-306.

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