On the structure of Borel ideals in-between the ideals <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi mathvariant="script">ED</mml:mi></mml:math> and Fin ⊗ Fin in the Katětov order

Das, Pratulananda; Filipów, Rafał; Głąb, Szymon; Tryba, Jacek

doi:10.1016/j.apal.2021.102976

Annals of Pure and Applied Logic

2021

DOI: 10.1016/j.apal.2021.102976

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On the structure of Borel ideals in-between the ideals ED and Fin ⊗ Fin in the Katětov order

Pratulananda Das

Rafał Filipów

Szymon Głąb

et al.

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2024

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Katětov order between Hindman, Ramsey and summable ideals

Filipów,

Kowitz,

Kwela

2024

Arch. Math. Logic

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A family $$\mathcal {I}$$ I of subsets of a set X is an ideal on X if it is closed under taking subsets and finite unions of its elements. An ideal $$\mathcal {I}$$ I on X is below an ideal $$\mathcal {J}$$ J on Y in the Katětov order if there is a function $$f{: }Y\rightarrow X$$ f : Y → X such that $$f^{-1}[A]\in \mathcal {J}$$ f - 1 [ A ] ∈ J for every $$A\in \mathcal {I}$$ A ∈ I . We show that the Hindman ideal, the Ramsey ideal and the summable ideal are pairwise incomparable in the Katětov order, where The Ramsey ideal consists of those sets of pairs of natural numbers which do not contain a set of all pairs of any infinite set (equivalently do not contain, in a sense, any infinite complete subgraph), The Hindman ideal consists of those sets of natural numbers which do not contain any infinite set together with all finite sums of its members (equivalently do not contain IP-sets that are considered in Ergodic Ramsey theory), The summable ideal consists of those sets of natural numbers such that the series of the reciprocals of its members is convergent.

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Katětov order between Hindman, Ramsey and summable ideals

Filipów,

Kowitz,

Kwela

2024

Arch. Math. Logic

Self Cite

View full text Add to dashboard Cite

show abstract

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On the structure of Borel ideals in-between the ideals ED and Fin ⊗ Fin in the Katětov order

Cited by 1 publication

References 29 publications

Katětov order between Hindman, Ramsey and summable ideals

Katětov order between Hindman, Ramsey and summable ideals

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On the structure of Borel ideals in-between the ideals ED and Fin ⊗ Fin in the Katětov order

Cited by 1 publication

References 29 publications

Katětov order between Hindman, Ramsey and summable ideals

Katětov order between Hindman, Ramsey and summable ideals

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On the structure of Borel ideals in-between the ideals ED and Fin ⊗ Fin in the Katětov order