On strong chains of sets and functions

Tanmay C. Inamdar

doi:10.1112/mtk.12183

On strong chains of sets and functions

Tanmay C. Inamdar

Department of Mathematics

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

Abstract

Shelah has shown that there are no chains of length ω₃ increasing modulo finite in (Formula presented.). We improve this result to sets. That is, we show that there are no chains of length ω₃ in (Formula presented.) increasing modulo finite. This contrasts with results of Koszmider who has shown that there are, consistently, chains of length ω₂ increasing modulo finite in (Formula presented.) as well as in (Formula presented.). More generally, we study the depth of function spaces (Formula presented.) quotiented by the ideal (Formula presented.) where (Formula presented.) are infinite cardinals.

Original language	English
Pages (from-to)	286-301
Number of pages	16
Journal	Mathematika
Volume	69
Issue number	1
DOIs	https://doi.org/10.1112/mtk.12183
State	Published - Jan 2023

Bibliographical note

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© 2023 The Authors. Mathematika is copyright © University College London and published by the London Mathematical Society on behalf of University College London.

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On strong chains of sets and functions

Abstract

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