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arXiv:1402.4659 [math.LO]AbstractReferencesReviewsResources

Force a set model of $Z_3$ + Harrington's Principle

Yong Cheng

Published 2014-02-19, updated 2014-11-30Version 2

Let $Z_3$ denote $3^{rd}$ order arithmetic. Let Harrington's Principle, HP, denote the statement that there is a real $x$ such that every $x$--admissible ordinal is a cardinal in $L$. In this paper, assuming there exists a remarkable cardinal with a weakly inaccessible cardinal above it, we force a set model of $Z_3\, + \, {\sf HP}$ via set forcing without reshaping.

Comments: 17 pages, revised and accepted version
Categories: math.LO
Subjects: 03E35, 03E55, 03E30
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