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august 2010 A formula that maps elements to proper classes in an arbitrary $\in$-universe
Olivier Esser
Bull. Belg. Math. Soc. Simon Stevin 17(3): 479-483 (august 2010). DOI: 10.36045/bbms/1284570733

Abstract

In this paper we construct a formula $\varphi(x,a)$ on the language of set theory $\mathcal{L}\mathbin{:}(\in,=)$ such that $\{x\ | \ \varphi(x,a)\}$ is a proper class for each element $a$ and such that if $a\neq a'$, the classes $\{x\ | \ \varphi(x,a)\}$ and $\{x\ | \ \varphi(x,a')\}$ are different. This formula works for any structure with the exception of 2 structures with two elements each. This formula ``maps'' elements to proper classes injectively.

Citation

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Olivier Esser. "A formula that maps elements to proper classes in an arbitrary $\in$-universe." Bull. Belg. Math. Soc. Simon Stevin 17 (3) 479 - 483, august 2010. https://doi.org/10.36045/bbms/1284570733

Information

Published: august 2010
First available in Project Euclid: 15 September 2010

zbMATH: 1207.03069
MathSciNet: MR2731369
Digital Object Identifier: 10.36045/bbms/1284570733

Subjects:
Primary: 03E99

Keywords: proper classes , Russell's paradox , Set theory

Rights: Copyright © 2010 The Belgian Mathematical Society

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Vol.17 • No. 3 • august 2010
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