J. von Neumann, Eine Axiomatisierung der Mengenlehre, Journal fur die reine und angewandte Mathematik, 154, 1925. Home/Search Document Not in Database Summary Related Articles Check |
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Grundlagenstreit in the Theory of Programming - Voda (2003) (Correct)
....is natural. In set theory, functions are a derived concept and it is tedious to have to derive basic laws like conversions [7] But (continuous) functions are no less pervasive concept in analysis, and von Neumann s formulation of set theory with functions as primitive notwithstanding [9], we use sets today because they are so much simpler to work with. The semantics of functions (i.e. that they are certain sets of pairs) can be divorced without any diculties whatsoever from the way we compute them (see [16] reduction, after all, amounts to nothing else than the use of the ....
J. von Neumann, Eine Axiomatisierung der Mengenlehre, Journal fur die reine und angewandte Mathematik, 154, 1925.
The Impact of the Lambda Calculus in Logic and Computer Science - Barendregt (1997) (8 citations) (Correct)
....Thesis by showing that the lambda definable functions coincide with the # recursive ones. 2 G odel just had given a series of lectures in Princeton at which Kleene and Rosser were present. 3 Consistent theories based on functions for the foundations of mathematics have been described by [89] (simplified by [98] With a similar aim are the theories in [53] and [75] In all these theories the paradoxes have been avoided by having a partial application. 43] 44] and [16] also discuss formal theories with partial application; they aim at constructive foundations and come close to ....
J. von Neumann, Eine axiomatisierung der mengenlehre, Journal f ur die Reine und Angewandte Mathematik, vol. 154 (1925), pp. 219--240.
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