This article is cited in 3 papers

Dialog theory of proofs for arithmetics, analysis and set theory

V. A. Yankov


Abstract: It is shown that in impredicative extensions of intuitionistic arithmetic, “intuitionistic” analysis, and “intuitionistic” Zermelo–Fraenkel set theory with the help of suitable “bar” axioms it is possible to show the consistency of classical arithmetic, classical analysis, and classical set theory. It is argued that the proofs given enable one to verify the true consistency of the classical systems.

UDC: 517.11

MSC: Primary 03F03, 03F55; Secondary 03E35, 03F10, 03E30, 03B20

Received: 02.07.1992

 English version: Russian Academy of Sciences. Izvestiya Mathematics, 1995, 44:3, 571–600

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