More conservativity for weak Kőnig's lemma
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916529386291200 |
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| author | Freund, Anton Uftring, Patrick |
| author_facet | Freund, Anton Uftring, Patrick |
| contents | We prove conservativity results for weak Kőnig's lemma that extend the celebrated result of Harrington (for $Π^1_1$-statements) and are somewhat orthogonal to the extension by Simpson, Tanaka and Yamazaki (for statements of the form $\forall X\exists!Yψ$ with arithmetical $ψ$). In particular, we show that $\mathsf{WKL}_0$ is conservative over $\mathsf{RCA}_0$ for well-ordering principles. We also show that compactness (which characterizes weak Kőnig's lemma) is dispensable for certain results about continuous functions with isolated singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20591 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More conservativity for weak Kőnig's lemma Freund, Anton Uftring, Patrick Logic 03B30, 03C25, 03D80, 03F35 We prove conservativity results for weak Kőnig's lemma that extend the celebrated result of Harrington (for $Π^1_1$-statements) and are somewhat orthogonal to the extension by Simpson, Tanaka and Yamazaki (for statements of the form $\forall X\exists!Yψ$ with arithmetical $ψ$). In particular, we show that $\mathsf{WKL}_0$ is conservative over $\mathsf{RCA}_0$ for well-ordering principles. We also show that compactness (which characterizes weak Kőnig's lemma) is dispensable for certain results about continuous functions with isolated singularities. |
| title | More conservativity for weak Kőnig's lemma |
| topic | Logic 03B30, 03C25, 03D80, 03F35 |
| url | https://arxiv.org/abs/2410.20591 |