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Remark on a system of bernays

Published online by Cambridge University Press:  12 March 2014

John Myhill
John Myhill*
Affiliation:
Stanford University, California
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Extract

In [1], Bemays gives an axiomatization of set-theory which represents the furthest development to date of the Zermelo-Frankel-Gödel tradition. The purpose of this note is to show that one of his axioms is redundant.

Primitives are ∈, set-abstraction (denoted [x/A(x)]) and the Hilbert selector (denoted σ). Different styles are used for free variables (a, b,c, …) and bound variables (x, y, z, …); both kinds of variables range over both sets and classes. Quantifiers and connectives are classical.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 28 , Issue 1 , March 1963 , pp. 75 - 76
Copyright
Copyright © Association for Symbolic Logic 1964

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References

[1]Bernays, P., Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, Essays on the Foundations of Mathematics, Dedicated to ProfessorFraenkel, A. H. on his 70th birthday. Magnes Press, The Hebrew University, Jerusalem, 1961, 49 pp.Google Scholar