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arXiv · 1402.4659

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

Yong Cheng
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Abstract

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.

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Yong Cheng. 2014-02-19. Force a set model of $Z_3$ + Harrington's Principle. https://doi.org/10.1002/malq.201300072

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