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/Summer 1994 A Dilemma in the Philosophy of Set Theory
Ralf-Dieter Schindler
Notre Dame J. Formal Logic 35(3): 458-463 (/Summer 1994). DOI: 10.1305/ndjfl/1040511351

Abstract

We show that the following conjecture about the universe V of all sets is wrong: for all set-theoretical (i.e., first order) schemata $\Sigma$ true in V there is a transitive set $\Sigma$ "reflecting" $\Sigma$ in such a way that the second order statement $\sigma$ corresponding to $\Sigma$ is true in $u$. More generally, we indicate the ontological commitments of any theory that exploits reflection principles in order to yield large cardinals. The disappointing conclusion will be that our only apparently good arguments for the existence of large cardinals have bad presuppositions.

Citation

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Ralf-Dieter Schindler. "A Dilemma in the Philosophy of Set Theory." Notre Dame J. Formal Logic 35 (3) 458 - 463, /Summer 1994. https://doi.org/10.1305/ndjfl/1040511351

Information

Published: /Summer 1994
First available in Project Euclid: 21 December 2002

zbMATH: 0832.03026
MathSciNet: MR1326127
Digital Object Identifier: 10.1305/ndjfl/1040511351

Subjects:
Primary: 03A05
Secondary: 00A30, 03E30, 03E55

Rights: Copyright © 1994 University of Notre Dame

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Vol.35 • No. 3 • /Summer 1994
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