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- W2140635086 abstract "Let C be an axiom system formalized within the first order functional calculus, and let C ′ be related to C as the Bernays-Gödel set theory is related to the Zermelo-Fraenkel set theory. (An exact definition of C ′ will be given later.) Ilse Novak [5] and Mostowski [8] have shown that, if C is consistent, then C ′ is consistent. (The converse is obvious.) Mostowski has also proved the stronger result that any theorem of C ′ which can be formalized in C is a theorem of C . The proofs of Novak and Mostowski do not provide a direct method for obtaining a contradiction in C from a contradiction in C ′. We could, of course, obtain such a contradiction by proving the theorems of C one by one; the above result assures us that we must eventually obtain a contradiction. A similar process is necessary to obtain the proof of a theorem in C from its proof in C ′. The purpose of this paper is to give a new proof of these theorems which provides a direct method of obtaining the desired contradiction or proof. The advantage of the proof may be stated more specifically by arithmetizing the syntax of C and C ′." @default.
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- W2140635086 date "1954-03-01" @default.
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- W2140635086 title "A relative consistency proof" @default.
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- W2140635086 doi "https://doi.org/10.2307/2267646" @default.
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