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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GF15-34700L" target="_blank" >GF15-34700L: Kontinuum, forcing a velké kardinály</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archive for Mathematical Logic

ISSN

0933-5846

e-ISSN

—

Svazek periodika

55

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

12

Strana od-do

493-504

Kód UT WoS článku

000374969600010

EID výsledku v databázi Scopus

2-s2.0-84964684012