There are no P-points in Silver extensions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F19%3A00507734" target="_blank" >RIV/67985840:_____/19:00507734 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s11856-019-1886-2" target="_blank" >http://dx.doi.org/10.1007/s11856-019-1886-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11856-019-1886-2" target="_blank" >10.1007/s11856-019-1886-2</a>

Result language
angličtina
Original language name
There are no P-points in Silver extensions
Original language description
We prove that after adding a Silver real no ultrafilter from the ground model can be extended to a P-point, and this remains to be the case in any further extension which has the Sacks property. We conclude that there are no P-points in the Silver model. In particular, it is possible to construct a model without P-points by iterating Borel partial orders. This answers a question of Michael Hrusak. We also show that the same argument can be used for the side-by-side product of Silver forcing. This provides a model without P-points with the continuum arbitrary large, answering a question of Wolfgang Wohofsky.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)