Inexpressibility results for ideals on countable sets and of compact sets

Jialiang He; Shuguo Zhang; Jiaheng Zhuang

doi:10.1016/j.apal.2026.103744

Inexpressibility results for ideals on countable sets and of compact sets

Jialiang He
, Shuguo Zhang
, Jiaheng Zhuang

Sichuan University

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a new method for constructing ideals on countable sets. As an application, we prove the existence of a [Figure presented] ideal of compact sets that is not expressible as a countable union of hereditary G_δ sets, thereby answering a question posed by É. Matheron and M. Zelený. Furthermore, we apply this construction to investigate Farah's conjecture, obtaining several new partial results.

Original language	English
Article number	103744
Journal	Annals of Pure and Applied Logic
Volume	177
Issue number	8
DOIs	https://doi.org/10.1016/j.apal.2026.103744
State	Published - 1 Aug 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2026 Elsevier B.V.

Keywords

Borel complexity
Ideal-friendly assignment
Ideals
Weakly Farah

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10.1016/j.apal.2026.103744

Cite this

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KW - Borel complexity

KW - Ideal-friendly assignment

KW - Ideals

KW - Weakly Farah

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Inexpressibility results for ideals on countable sets and of compact sets

Abstract

Bibliographical note

Keywords

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