On extendability to $F_\sigma$ ideals
Adam Kwela
TL;DR
This paper constructs a specific Borel ideal that cannot be extended to any $F_\sigma$ ideal and is not Kat10ov above the convex ideal, answering a question posed by M. Hru61E1k.
Contribution
It provides a counterexample of a Borel ideal with particular extendability properties, advancing understanding of ideal extendability in descriptive set theory.
Findings
Constructed a Borel ideal not extendable to any $F_\sigma$ ideal.
Showed the ideal is not Kat10ov above the convex ideal.
Answered negatively a question of M. Hru61E1k.
Abstract
Answering in negative a question of M. Hru\v{s}\'ak, we construct a Borel ideal not extendable to any ideal and such that it is not Kat\v{e}tov above the ideal .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory