Spectrum of FO logic with quantifier depth 4 is finite
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909072364666880 |
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| author | Yarovikov, Yury Zhukovskii, Maksim |
| author_facet | Yarovikov, Yury Zhukovskii, Maksim |
| contents | The $k$-spectrum is the set of all $α>0$ such that $G(n,n^{-α})$ does not obey the 0-1 law for FO sentences with quantifier depth at most $k$. In this paper, we prove that the minimum $k$ such that the $k$-spectrum is infinite equals 5. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_11470 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Spectrum of FO logic with quantifier depth 4 is finite Yarovikov, Yury Zhukovskii, Maksim Combinatorics The $k$-spectrum is the set of all $α>0$ such that $G(n,n^{-α})$ does not obey the 0-1 law for FO sentences with quantifier depth at most $k$. In this paper, we prove that the minimum $k$ such that the $k$-spectrum is infinite equals 5. |
| title | Spectrum of FO logic with quantifier depth 4 is finite |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2111.11470 |