Ultrafilters and Decompositions of Abelian Groups
We prove that every PS-ultrafilter on a group without second-order elements is a Ramsey ultrafilter. For an arbitrary PS-ultrafilter ϕ on a countable group G, we construct a mapping f: G → ω such that f(ϕ) is a P-point in the space ω*. We determine a new class of subselective ultrafilters, which is...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4224 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510355699007488 |
|---|---|
| author | Protasov, I. V. Протасов, И. В. Протасов, И. В. |
| author_facet | Protasov, I. V. Протасов, И. В. Протасов, И. В. |
| author_sort | Protasov, I. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:00Z |
| description | We prove that every PS-ultrafilter on a group without second-order elements is a Ramsey ultrafilter. For an arbitrary PS-ultrafilter ϕ on a countable group G, we construct a mapping f: G → ω such that f(ϕ) is a P-point in the space ω*. We determine a new class of subselective ultrafilters, which is considerably wider than the class of PS-ultrafilters. |
| first_indexed | 2026-03-24T02:55:41Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4224 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:55:41Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/8d/34e81941593107a09ee969d72464d68d.pdf |
| spelling | umjimathkievua-article-42242020-03-18T20:25:00Z Ultrafilters and Decompositions of Abelian Groups Ультрафильтры и разбиения абелевых групп Protasov, I. V. Протасов, И. В. Протасов, И. В. We prove that every PS-ultrafilter on a group without second-order elements is a Ramsey ultrafilter. For an arbitrary PS-ultrafilter ϕ on a countable group G, we construct a mapping f: G → ω such that f(ϕ) is a P-point in the space ω*. We determine a new class of subselective ultrafilters, which is considerably wider than the class of PS-ultrafilters. Доведено, що кожен PS -ультрафільтр на групі без елементів порядку 2 рамсеїв. Для довільного PS-ультрафільтра (ϕ на зліченній групі G побудовано відображення f: G → ω таке, що $f(ϕ)$ — P-точка у просторі ω*. Визначено новий клас субселективних ультрафільтрів, значно ширший за клас PS-ультрафільтрів. Institute of Mathematics, NAS of Ukraine 2001-01-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4224 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 1 (2001); 85-93 Український математичний журнал; Том 53 № 1 (2001); 85-93 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4224/5152 https://umj.imath.kiev.ua/index.php/umj/article/view/4224/5153 Copyright (c) 2001 Protasov I. V. |
| spellingShingle | Protasov, I. V. Протасов, И. В. Протасов, И. В. Ultrafilters and Decompositions of Abelian Groups |
| title | Ultrafilters and Decompositions of Abelian Groups |
| title_alt | Ультрафильтры и разбиения абелевых групп |
| title_full | Ultrafilters and Decompositions of Abelian Groups |
| title_fullStr | Ultrafilters and Decompositions of Abelian Groups |
| title_full_unstemmed | Ultrafilters and Decompositions of Abelian Groups |
| title_short | Ultrafilters and Decompositions of Abelian Groups |
| title_sort | ultrafilters and decompositions of abelian groups |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4224 |
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