P-measures in models without P-points

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00618224" target="_blank" >RIV/67985840:_____/25:00618224 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.apal.2025.103579" target="_blank" >https://doi.org/10.1016/j.apal.2025.103579</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apal.2025.103579" target="_blank" >10.1016/j.apal.2025.103579</a>

Result language
angličtina
Original language name
P-measures in models without P-points
Original language description
We answer in negative the problem if the existence of a P-measure implies the existence of a P-point. Namely, we show that if we add random reals to a certain ‘unique P-point’ model, then in the resulting model we will have a P-measure but not P-points. Also, we investigate the question if there is a P-measure in the Silver model. We show that rapid filters cannot be extended to a P-measure in the extension by ω product of Silver forcings and that in the model obtained by the countable support omega_2-iteration of countable product of Silver forcings there are no P-measures of countable Maharam type.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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