Ideal Analytic sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918374353666048 |
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| author | Mazurkiewicz, Łukasz Żeberski, Szymon |
| author_facet | Mazurkiewicz, Łukasz Żeberski, Szymon |
| contents | The aim of this paper is to give natural examples of $\mathbfΣ_1^1$-complete and $\mathbfΠ_1^1$-complete sets.
In the first part, we consider ideals on $ω$. In particular, we show that the Hindman ideal $\mathcal{H}$ is $\mathbfΠ_1^1$-complete and consider a number of ideals generated in the similar fashion. Moreover, we show that the ideal $\mathcal{D}$ is also $\mathbfΠ_1^1$-complete.
In the second part, we focus on families of trees (on $ω$ and $2$) containing a specific tree type. We show the connection between two topics and explore some classical tree types (like Sacks and Miller). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_07693 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ideal Analytic sets Mazurkiewicz, Łukasz Żeberski, Szymon Logic General Topology 03E75, 28A05, 54H05 (Primary), 03E17 (Secondary) The aim of this paper is to give natural examples of $\mathbfΣ_1^1$-complete and $\mathbfΠ_1^1$-complete sets. In the first part, we consider ideals on $ω$. In particular, we show that the Hindman ideal $\mathcal{H}$ is $\mathbfΠ_1^1$-complete and consider a number of ideals generated in the similar fashion. Moreover, we show that the ideal $\mathcal{D}$ is also $\mathbfΠ_1^1$-complete. In the second part, we focus on families of trees (on $ω$ and $2$) containing a specific tree type. We show the connection between two topics and explore some classical tree types (like Sacks and Miller). |
| title | Ideal Analytic sets |
| topic | Logic General Topology 03E75, 28A05, 54H05 (Primary), 03E17 (Secondary) |
| url | https://arxiv.org/abs/2310.07693 |