Easton functions and supercompactness
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Easton functions and supercompactness
Original language description
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)
Czech name
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Czech description
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Classification
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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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Fundamenta Mathematicae
ISSN
0016-2736
e-ISSN
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Volume of the periodical
226
Issue of the periodical within the volume
3
Country of publishing house
PL - POLAND
Number of pages
17
Pages from-to
279-296
UT code for WoS article
000342334000006
EID of the result in the Scopus database
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