Ideal Topologies in Higher Descriptive Set Theory

Peter Holy; Marlene Koelbing; Philipp Schlicht; Wolfgang Wohofsky

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arXiv · 2111.07339

Ideal Topologies in Higher Descriptive Set Theory

Peter Holy·Marlene Koelbing·Philipp Schlicht·Wolfgang Wohofsky

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Abstract

We investigate generalizations of the topology of the higher Cantor space on $2^\kappa$, based on arbitrary ideals rather than the bounded ideal on $\kappa$. Our main focus is on the topology induced by the nonstationary ideal, and we call this topology the nonstationary topology, or also the Edinburgh topology on $2^\kappa$. It may be of independent interest that as a side result, we show $\kappa$-Silver forcing to satisfy a strong form of Axiom $A$ not only if $\kappa$ is inaccessible (which is well-known), but also under the assumption $\diamondsuit_\kappa$.

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BibTeX RIS

Peter Holy, Marlene Koelbing, Philipp Schlicht, Wolfgang Wohofsky. 2021-11-14. Ideal Topologies in Higher Descriptive Set Theory. https://arxiv.org/abs/2111.07339

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