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| Main Author: | |
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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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| _version_ | 1866912618879385600 |
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| author | Cheng, Yong |
| author_facet | Cheng, Yong |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1402_4659 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Force a set model of $Z_3$ + Harrington's Principle Cheng, Yong Logic 03E35, 03E55, 03E30 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. |
| title | Force a set model of $Z_3$ + Harrington's Principle |
| topic | Logic 03E35, 03E55, 03E30 |
| url | https://arxiv.org/abs/1402.4659 |