Locally countable graphs of second projective class not generated by countably many projective functions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914598705168384 |
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| author | Kanovei, Vladimir Lyubetsky, Vassily |
| author_facet | Kanovei, Vladimir Lyubetsky, Vassily |
| contents | To answer a question by Rettich and Serafin, we define a model of set theory in which there exists a locally countable $\varPi^1_2$ graph on a subset of the real line, which is not generated by a countable family of projective (or even real-ordinal definable, ROD) functions. We also prove that the $\varSigma^1_2$ equi-constructibility graph on the reals is not generated by a countable family of ROD functions in the Solovay model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03126 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locally countable graphs of second projective class not generated by countably many projective functions Kanovei, Vladimir Lyubetsky, Vassily Logic 03E15, 03E35, 03E45 To answer a question by Rettich and Serafin, we define a model of set theory in which there exists a locally countable $\varPi^1_2$ graph on a subset of the real line, which is not generated by a countable family of projective (or even real-ordinal definable, ROD) functions. We also prove that the $\varSigma^1_2$ equi-constructibility graph on the reals is not generated by a countable family of ROD functions in the Solovay model. |
| title | Locally countable graphs of second projective class not generated by countably many projective functions |
| topic | Logic 03E15, 03E35, 03E45 |
| url | https://arxiv.org/abs/2605.03126 |