Easton's theorem and large cardinals from the optimal hypothesis

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Easton's theorem and large cardinals from the optimal hypothesis
Original language description
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
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/GP201%2F09%2FP115" target="_blank" >GP201/09/P115: Logical and set-theoretical properties of the continuum function</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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