The fine structure of operator mice
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2016
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| _version_ | 1866909607903887360 |
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| author | Schlutzenberg, Farmer Trang, Nam |
| author_facet | Schlutzenberg, Farmer Trang, Nam |
| contents | We develop the fine structure theory of operator-premice. These are a generalization of standard premice, in which an abstract operator $F$ is used to form the successor steps in the internal hierarchy of the premouse, instead of Jensen's $J$-operator (which computes rudimentary closure). Such notions have seen applications in core model induction arguments, but their theory has not previously been developed in detail. We define fine condensation for operators $F$ and show that fine condensation and iterability together ensure that $F$-mice have the fundamental fine structural properties including universality and solidity of the standard parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1604_00083 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | The fine structure of operator mice Schlutzenberg, Farmer Trang, Nam Logic 03E45, 03E55 We develop the fine structure theory of operator-premice. These are a generalization of standard premice, in which an abstract operator $F$ is used to form the successor steps in the internal hierarchy of the premouse, instead of Jensen's $J$-operator (which computes rudimentary closure). Such notions have seen applications in core model induction arguments, but their theory has not previously been developed in detail. We define fine condensation for operators $F$ and show that fine condensation and iterability together ensure that $F$-mice have the fundamental fine structural properties including universality and solidity of the standard parameter. |
| title | The fine structure of operator mice |
| topic | Logic 03E45, 03E55 |
| url | https://arxiv.org/abs/1604.00083 |