Easton's theorem and large cardinals from the optimal hypothesis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F12%3A10127050" target="_blank" >RIV/00216208:11210/12:10127050 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.apal.2012.04.002" target="_blank" >http://dx.doi.org/10.1016/j.apal.2012.04.002</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.apal.2012.04.002" target="_blank" >10.1016/j.apal.2012.04.002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Easton's theorem and large cardinals from the optimal hypothesis

Popis výsledku v původním jazyce

The equiconsistency of a measurable cardinal with Mitchell order $o(kappa) = kappa^{++}$ with a measurable cardinal such that $2^kappa = kappa^{++}$ follows from the results by W.~Mitchell cite{MITcoreI} and M.~Gitik cite{GITIKo2}. These results were later generalized to measurable cardinals with $2^kappa$ larger than $kappa^{++}$ (see cite{GITIKmeasure}). In cite{RADEKeaston}, we formulated and proved Easton's theorem cite{EASTONregular} in a large cardinal setting, using slightly stronger hypotheses than the lower bounds identified by Mitchell and Gitik (we used the assumption that the relevant target model contains $H(mu)$, for a suitable $mu$, instead of the cardinals with the appropriate Mitchell order). In this paper, we use a new idea which allows us to carry out the constructions in cite{RADEKeaston} from the optimal hypotheses. It follows that the lower bounds identified by Mitchell and Gitik are optimal also with regard to the general behaviour of the continuum

Název v anglickém jazyce

Easton's theorem and large cardinals from the optimal hypothesis

Popis výsledku anglicky

The equiconsistency of a measurable cardinal with Mitchell order $o(kappa) = kappa^{++}$ with a measurable cardinal such that $2^kappa = kappa^{++}$ follows from the results by W.~Mitchell cite{MITcoreI} and M.~Gitik cite{GITIKo2}. These results were later generalized to measurable cardinals with $2^kappa$ larger than $kappa^{++}$ (see cite{GITIKmeasure}). In cite{RADEKeaston}, we formulated and proved Easton's theorem cite{EASTONregular} in a large cardinal setting, using slightly stronger hypotheses than the lower bounds identified by Mitchell and Gitik (we used the assumption that the relevant target model contains $H(mu)$, for a suitable $mu$, instead of the cardinals with the appropriate Mitchell order). In this paper, we use a new idea which allows us to carry out the constructions in cite{RADEKeaston} from the optimal hypotheses. It follows that the lower bounds identified by Mitchell and Gitik are optimal also with regard to the general behaviour of the continuum

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/GP201%2F09%2FP115" target="_blank" >GP201/09/P115: Logické a množinově-teoretické vlastnosti funkce kontinua</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Annals of Pure and Applied Logic

ISSN

0168-0072

e-ISSN

—

Svazek periodika

163

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

1738-1747

Kód UT WoS článku

000309300300002

EID výsledku v databázi Scopus

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