Abstract
In this paper we study the role of functioning axioms on the deductive power of the system obtained from the Zermelo-Fraenkel ZF system by the introduction of ɛ-terms with the possibility of using them as a scheme for the substitution axiom. It is proved that if the system has a founding axiom the introduction of ɛ-terms does not extend the class of ZF theorems, while if the founding axiom is absent, there is an extension of the ZF theorems.
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Literature cited
A. C. Leisenring, Mathematical Logic and Hilbert's ɛ-symbol, London (1969).
P. J. Cohen, Set Theory and the Continuum Hypothesis [Russian translation], Moscow (1969).
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Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 569–575, November, 1972.
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Grishin, V.N. The theory of Zermelo-Fraenkel sets with Hilbert ɛ-terms. Mathematical Notes of the Academy of Sciences of the USSR 12, 779–783 (1972). https://doi.org/10.1007/BF01099064
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DOI: https://doi.org/10.1007/BF01099064