Easton functions and supercompactness

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F14%3A10289626" target="_blank" >RIV/00216208:11210/14:10289626 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4064/fm226-3-6" target="_blank" >http://dx.doi.org/10.4064/fm226-3-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/fm226-3-6" target="_blank" >10.4064/fm226-3-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Easton functions and supercompactness

Popis výsledku v původním jazyce

Suppose that kappa is lambda-supercompact witnessed by an elementary embedding j : V -> M with critical point kappa, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton's theorem: (1) for all alpha alpha < cf(F(alpha)), and (2) alpha < beta double right arrow F(alpha) {= F(beta). We address the question: assuming GCH, what additional assumptions are necessary on j and F if one wants to be able to force the continuumfunction to agree with F globally, while preserving the lambda-supercompactness of kappa? We show that, assuming GCH, if F is any function as above, and in addition for some regular cardinal lambda> kappa there is an elementary embedding j : V -> M withcritical point kappa such that kappa is is closed under F, the model M is closed under lambda-sequences, H(F(lambda)) subset of M, and for each regular cardinal gamma {= lambda one has (vertical bar j(F)(gamma)vertical bar = F(gamma))(V)

Název v anglickém jazyce

Easton functions and supercompactness

Popis výsledku anglicky

Suppose that kappa is lambda-supercompact witnessed by an elementary embedding j : V -> M with critical point kappa, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton's theorem: (1) for all alpha alpha < cf(F(alpha)), and (2) alpha < beta double right arrow F(alpha) {= F(beta). We address the question: assuming GCH, what additional assumptions are necessary on j and F if one wants to be able to force the continuumfunction to agree with F globally, while preserving the lambda-supercompactness of kappa? We show that, assuming GCH, if F is any function as above, and in addition for some regular cardinal lambda> kappa there is an elementary embedding j : V -> M withcritical point kappa such that kappa is is closed under F, the model M is closed under lambda-sequences, H(F(lambda)) subset of M, and for each regular cardinal gamma {= lambda one has (vertical bar j(F)(gamma)vertical bar = F(gamma))(V)

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

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název periodika

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

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Svazek periodika

226

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

17

Strana od-do

279-296

Kód UT WoS článku

000342334000006

EID výsledku v databázi Scopus

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