Mathias-Prikry and Laver type forcing; Summable ideals, coideals, and +-selective filters

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F16%3A00458990" target="_blank" >RIV/67985840:_____/16:00458990 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00153-016-0476-9" target="_blank" >http://dx.doi.org/10.1007/s00153-016-0476-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00153-016-0476-9" target="_blank" >10.1007/s00153-016-0476-9</a>

Result language
angličtina
Original language name
Mathias-Prikry and Laver type forcing; Summable ideals, coideals, and +-selective filters
Original language description
We study the Mathias–Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias–Prikry forcings with summable ideals are all mutually bi-embeddable. We show that Mathias forcing associated with the complement of an analytic ideal always adds a dominating real. We also characterize filters for which the associated Mathias–Prikry forcing does not add eventually different reals, and show that they are countably generated provided they are Borel. We give a characterization of omega-hitting and omega-splitting families which retain their property in the extension by a Laver type forcing associated with a coideal.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GF15-34700L" target="_blank" >GF15-34700L: The continuum, forcing and large cardinals</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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