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Philosophia Mathematica Advance Access originally published online on January 30, 2006
Philosophia Mathematica 2006 14(2):153-188; doi:10.1093/philmat/nkj009
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Philosophia Mathematica (III), Vol. 14 No. 2 © The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

On the Question of Absolute Undecidability{dagger}

Peter Koellner*

* Department of Philosophy, Emerson Hall, Harvard University Cambridge, Massachusetts 02138, U. S. A. koellner{at}fas.harvard.edu

The paper begins with an examination of Gödel's views on absolute undecidability and related topics in set theory. These views are sharpened and assessed in light of recent developments. It is argued that a convincing case can be made for axioms that settle many of the questions undecided by the standard axioms and that in a precise sense the program for large cardinals is a complete success "below" CH. It is also argued that there are reasonable scenarios for settling CH and that there is not currently a convincing case to the effect that a given statement is absolutely undecidable.


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