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arXiv · 2310.07693

Ideal Analytic sets

Łukasz Mazurkiewicz·Szymon Żeberski
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Abstract

The aim of this paper is to give natural examples of $\mathbf{\Sigma}_1^1$-complete and $\mathbf{\Pi}_1^1$-complete sets. In the first part, we consider ideals on $\omega$. In particular, we show that the Hindman ideal $\mathcal{H}$ is $\mathbf{\Pi}_1^1$-complete and consider a number of ideals generated in the similar fashion. Moreover, we show that the ideal $\mathcal{D}$ is also $\mathbf{\Pi}_1^1$-complete. In the second part, we focus on families of trees (on $\omega$ and $2$) containing a specific tree type. We show the connection between two topics and explore some classical tree types (like Sacks and Miller).

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BibTeXRIS

Łukasz Mazurkiewicz, Szymon Żeberski. 2023-10-11. Ideal Analytic sets. https://doi.org/10.1002/malq.70012

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