Filtry
I-ultrafilters and summable ideals
We study I-ultrafilters and two weaker notions in the setting where I is a tall summable ideal Ig on the natural numbers. Such ultrafilters are closely related to rapid ultrafilters. We consider various aspects of this rela...
BA - Obecná matematika
- 2010 •
- D
Rok uplatnění
D - Stať ve sborníku
Generic existence of ultrafilters on the natural numbers
Say that a class of ultrafilters exists generically if every filter base of size < c can be extended to an ultrafilter in that class. We investigate generic existence of ultrafilters defined in terms of ideals on the nat...
Pure mathematics
- 2017 •
- Jimp •
- Odkaz
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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Adding ultrafilters by definable quotients
Forcing notions of the type () which do not add reals naturally add ultrafilters on ?. We investigate what classes of ultrafilters can be added in this way when is a definable ideal. In particular, we show that if is an F ? P-ideal ...
BA - Obecná matematika
- 2011 •
- Jx •
- Odkaz
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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Ultrafilter selection and Corson compacta
generating set there is an ultrafilter selecting maximal number of its elements. We call it the ultrafilter selection property. For cardinality ℵ1 the property is equivalent to the fact that the space of ultrafilters is no...
Pure mathematics
- 2022 •
- Jimp •
- Odkaz
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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Coherent Ultrafilters and Nonhomogeneity
We introduce the notion of a coherent P-ultrafilter on a complete ccc Boolean that these ultrafilters exist generically under the assumption that the dominating numberis not less ultrafilters exist generically under c = cov...
BA - Obecná matematika
- 2015 •
- Jx •
- Odkaz
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
I-ultrafilters in the rational perfect set model
cardinality of a family D of tall summable ideals such that an ultrafilter is rapid-ideals such that |D| < d , there is an ultrafilter U which is an I -ultrafilter for all ideals I is an element of D at the same time, yet ...
Pure mathematics
- 2024 •
- Jimp •
- Odkaz
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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HL ideals and Sacks indestructible ultrafilters
We study ultrafilters on countable sets and reaping families which are indestructible by Sacks forcing. We deal with the combinatorial characterization indestructible ultrafilters and prove that every Sacks indestructible ultraf...
Pure mathematics
- 2024 •
- Jimp •
- Odkaz
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Ideals and their generic ultrafilters
Let I be an F-sigma-ideal on natural numbers. We characterize the ultrafilters which are generic over the model L(R) for the poset of I-positive sets of natural numbers ordered by inclusion....
Pure mathematics
- 2020 •
- Jimp •
- Odkaz
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
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A note on I-ultrafilters and P-points
We consider the question whether P-points can be characterized as I-ultrafilters for I an ideal on natural numbers and show that (consistently) it is not possible if I is an F_sigma-ideal or a P-ideal....
BA - Obecná matematika
- 2007 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Ultrafilter extensions of asymptotic density
We characterize for which ultrafilters on $omega$ is the ultrafilter extension of the asymptotic density on natural numbers $sigma$-additive on the quotient boolean algebra $mathcal{P}(omega)/d_{mathcal{U}}$ or satisfies similar add...
Pure mathematics
- 2019 •
- Jimp •
- Odkaz
Rok uplatnění
Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
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