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Mat. Zametki, 1972, Volume 12, Issue 5, Pages 569–575 (Mi mz9918)  

The theory of Zermelo-Fraenkel sets with Hilbert $\varepsilon$-terms

V. N. Grishin

M. V. Lomonosov Moscow State University

Abstract: In this paper we study the role of functioning axioms on the deductive power of the system obtained from the Zermelo–Fraenkel $\mathrm{ZF}$ system by the introduction of $\varepsilon$-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 $\varepsilon$-terms does not extend the class of $\mathrm{ZF}$ theorems, while if the founding axiom is absent, there is an extension of the $\mathrm{ZF}$ theorems.

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English version:
Mathematical Notes, 1972, 12:5, 779–783

Bibliographic databases:

Document Type: Article
UDC: 513
Received: 30.04.1971

Citation: V. N. Grishin, “The theory of Zermelo-Fraenkel sets with Hilbert $\varepsilon$-terms”, Mat. Zametki, 12:5 (1972), 569–575; Math. Notes, 12:5 (1972), 779–783

Citation in format AMSBIB
\Bibitem{Gri72}
\by V.~N.~Grishin
\paper The theory of Zermelo-Fraenkel sets with Hilbert $\varepsilon$-terms
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 5
\pages 569--575
\mathnet{http://mi.mathnet.ru/mz9918}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=316247}
\zmath{https://zbmath.org/?q=an:0246.02050}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 5
\pages 779--783
\crossref{https://doi.org/10.1007/BF01099064}


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