K. Godel, The consistency of the continuum hypothesis, Annals of mathematics studies no. 3. Princeton University Press, Princeton, N.J. 1940. Home/Search Document Not in Database Summary Related Articles Check |
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Grundlagenstreit in the Theory of Programming - Voda (2003) (Correct)
....programming are incautiously moving away from the standard mathematical practice with consequences that can harm only them. 3 Second Order Theory of Finite Sets: FSI We axiomatize the theory FSI of nite sets in the style of the set theory with classes of von Neumann, Bernays, and G odel (VBG) [6] as a two sorted ( rstorder) theory. Upper case variables range over the sort of classes and the lower case variables over the sort of ( nite) sets. There is a single non logical symbol 2 of class membership. The atomic formulas are 1 2 2 and 1 = 2 for any combination of set and class ....
....sets. The domain of classes is formed from those subsets of H which are de nable by comprehension from restricted formulas [x] with at most x free. There is nothing impredicative about the construction of the last domain. Its elements are generated from the class E by the Weyl G odel operators [4, 6] in arguments X and Y : X Y X Dom(X) V X X Cnv 1 (X) Cnv 2 (X) The operators satisfy: hx; yi 2 E x 2 y x 2 X Y x 2 X x 2 Y x 2 X x = 2 X x 2 Dom(X) 9y hy; xi 2 X hx; yi 2 V X y 2 X hx; yi 2 X hy; xi 2 X hx; y; zi 2 Cnv 1 (X) hy; z; xi 2 X hx; y; zi 2 Cnv ....
K. Godel, The consistency of the continuum hypothesis, Annals of mathematics studies no. 3. Princeton University Press, Princeton, N.J. 1940. Reprinted in K. Godel Collected Works vol 2., Oxford University press, 1990.
Predicative Justification and Development of a Second Order Theory .. - Voda (Correct)
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K. Godel, The consistency of the continuum hypothesis, Annals of mathematics studies no. 3. Princeton University Press, Princeton, N.J. 1940.
Truth Definitions, Skolem Functions And Axiomatic Set Theory - Hintikka (1998) (Correct)
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G odel, K., The consistency of the continuum hypothesis, Annals of Mathematical Studies, vol. 3, Princeton University Press, Princeton, 1940.
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