Read e-book online Logic, Methodology and Philosophy of Science VII, PDF

By Ruth Barcan-Marcus, George J. W. Dorn, Paul Weingartner

ISBN-10: 0444876561

ISBN-13: 9780444876560

BARCAN, R, / G, J, W, DORN / P, WEINGARTNER, EDS,: good judgment, method AND PHILOSOPHY OF technological know-how VII, complaints OF THE 7th foreign CONGRESS, SALZBURG, AUSTRIA, AMSTERDAM, 1986, xiv 738 p, Encuadernacion unique, Nuevo,

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Extra info for Logic, Methodology and Philosophy of Science VII, Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of Science

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As y is a base there is a function g: y ~ H (Y) such that 'Vx E y (f(x), g(x) E R. If b = ran g then bE H(Y) and 'Vx E a 3z E b (x, y) E R & 'Vz E b 3x E a (x, y) E R. 0 The next lemma will be needed to verify the restricted separation scheme in our inner models. 4. If Y is a nt-closed class of bases then for each restricted CONSTRUCTIVE SET THEORY 33 sentence ljJ with parameters in H( Y) there is a set c E Y such that ljJ == 3x (x E c). PROOF. c to abbreviate 3x(x E c). The following facts are easy to check if A, B are sets and B; is a set for each a E A.

Brouwer centenary symposium (North-Holland, Amsterdam). V. J. BEESON Dept. A. "Proving programs" is computer science; "programming proofs" is logic. The meeting ground of the two is that both depend on formal systems; those of logic are designed for proving, those of computer science are designed for programming. Future progress, in particular progress in applications to large-scale computer sytems, depends on the design of new formal systems. What should these be like and how might they be used?

1 Sublemma. For every nt-generated set A if x, yEA then l(x, y) E X. For if A E X then there is a nt-generated set b, c E A then by the Sublemma l(f(b ),f(c» E l(b, c) = I(f(b), f(c ». A = A. If as f is one-one A and f: x. But Proof of Sublemma. Let Y be the class of those nt-generated sets A such that if x, yEA then l(x, y) E X. It suffices to show that Y is nt-closed. Trivially 0 E Y and w E Y because if n, mEw then l(n, m) = {0} if n = m and 0 if n"l- m. In either case l(n, m) E X. Now suppose that A E Y and B; E Y for each a E A.

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Logic, Methodology and Philosophy of Science VII, Proceedings of the Seventh International Congress of Logic, Methodology and Philosophy of Science by Ruth Barcan-Marcus, George J. W. Dorn, Paul Weingartner


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