-ideals and -gaps in the Boolean algebras Ρ(ω)/I.
Krzysztof Mazur (1991)
Fundamenta Mathematicae
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Krzysztof Mazur (1991)
Fundamenta Mathematicae
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Gábor Czédli, Miklós Maróti (2010)
Mathematica Bohemica
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We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived.
Jörg Brendle, Diego Alejandro Mejía (2014)
Fundamenta Mathematicae
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The Rothberger number (ℐ) of a definable ideal ℐ on ω is the least cardinal κ such that there exists a Rothberger gap of type (ω,κ) in the quotient algebra (ω)/ℐ. We investigate (ℐ) for a class of ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is ℵ₁, while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even...
Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2011)
Czechoslovak Mathematical Journal
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We consider various forms of Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem which are connected with ideals of subsets of natural numbers. We characterize ideals with properties considered. We show that, in a sense, Ramsey's theorem, the monotone subsequence theorem and the Bolzano-Weierstrass theorem characterize the same class of ideals. We use our results to show some versions of density Ramsey's theorem (these are similar to generalizations...
Deng Yin Wang, Haishan Pan, Xuansheng Wang (2010)
Czechoslovak Mathematical Journal
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Let be an arbitrary parabolic subalgebra of a simple associative -algebra. The ideals of are determined completely; Each ideal of is shown to be generated by one element; Every non-linear invertible map on that preserves ideals is described in an explicit formula.
Alan Taylor (1980)
Fundamenta Mathematicae
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Rafał Filipów, Nikodem Mrożek, Ireneusz Recław, Piotr Szuca (2013)
Commentationes Mathematicae Universitatis Carolinae
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We show that the ideal of nowhere dense subsets of rationals cannot be extended to an analytic P-ideal, ideal nor maximal P-ideal. We also consider a problem of extendability to a non-meager P-ideals (in particular, to maximal P-ideals).