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| Format: | Preprint |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1402.4659 |
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Table of Contents:
- 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.