The transcendence degree of the reals over certain set-theoretical subfields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908757825421312 |
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| author | Fatalini, Azul Schindler, Ralf |
| author_facet | Fatalini, Azul Schindler, Ralf |
| contents | It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set $X$ of finitely many Cohen reals, by showing that, in the forcing extension, the transcendence degree of the reals over a combination of the reals in the extension given by each proper subset of $X$ is also maximal. This answers a question of Kanovei and Schindler. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00616 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The transcendence degree of the reals over certain set-theoretical subfields Fatalini, Azul Schindler, Ralf Logic Commutative Algebra It is a well-known result that, after adding one Cohen real, the transcendence degree of the reals over the ground-model reals is continuum. We extend this result for a set $X$ of finitely many Cohen reals, by showing that, in the forcing extension, the transcendence degree of the reals over a combination of the reals in the extension given by each proper subset of $X$ is also maximal. This answers a question of Kanovei and Schindler. |
| title | The transcendence degree of the reals over certain set-theoretical subfields |
| topic | Logic Commutative Algebra |
| url | https://arxiv.org/abs/2412.00616 |