Thin ultrafilters, P-hierarchu and MArtin Axiom
| Autor: | Machura, Michał, Starosolski, Andrzej |
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| Rok vydání: | 2012 |
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| Druh dokumentu: | Working Paper |
| Popis: | Under MA we prove that for the ideal $\cal I$ of thin sets on $\omega$ and for any ordinal $\gamma \leq \omega_1$ there is an ${\cal I}$-ultrafilter (in the sense of Baumgartner), which belongs to the class ${\cal P}_{\gamma}$ of P-hierarchy of ultrafilters. Since the class of ${\cal P}_2$ ultrafilters coincides with a class of P-points, out result generalize theorem of Fla\v{s}kov\'a, which states that there are ${\cal I}$-ultrafilters which are not P-points. It is also related to theorem which states that under CH for any tall P-ideal $\cal I$ on $\omega$ there is an ${\cal I}$-ultrafilter, however the ideal of thin sets is not P-ideal. Comment: 12 pages. arXiv admin note: substantial text overlap with arXiv:1108.1818 |
| Databáze: | arXiv |
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