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Statements

Subject Item
n2:RIV%2F00216208%3A11210%2F14%3A10289626%21RIV15-MSM-11210___
rdf:type
skos:Concept n19:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.4064/fm226-3-6
dcterms: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 continuum function 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 with critical 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), then there is a cardinal-preserving forcing extension in which 2(delta) = F(delta) for every regular cardinal delta and kappa remains lambda-supercornpact. This answers a question of [CM14]. 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 continuum function 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 with critical 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), then there is a cardinal-preserving forcing extension in which 2(delta) = F(delta) for every regular cardinal delta and kappa remains lambda-supercornpact. This answers a question of [CM14].
dcterms:title
Easton functions and supercompactness Easton functions and supercompactness
skos:prefLabel
Easton functions and supercompactness Easton functions and supercompactness
skos:notation
RIV/00216208:11210/14:10289626!RIV15-MSM-11210___
n3:aktivita
n17:I
n3:aktivity
I
n3:cisloPeriodika
3
n3:dodaniDat
n12:2015
n3:domaciTvurceVysledku
n8:3211800
n3:druhVysledku
n13:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n9:predkladatel
n3:idSjednocenehoVysledku
12834
n3:idVysledku
RIV/00216208:11210/14:10289626
n3:jazykVysledku
n14:eng
n3:klicovaSlova
Easton's theorem; continuum function; supercompactness
n3:klicoveSlovo
n4:continuum%20function n4:Easton%27s%20theorem n4:supercompactness
n3:kodStatuVydavatele
PL - Polská republika
n3:kontrolniKodProRIV
[1AC7AFDF3C9C]
n3:nazevZdroje
Fundamenta Mathematicae
n3:obor
n7:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n12:2014
n3:svazekPeriodika
226
n3:tvurceVysledku
Honzík, Radek Cody, Brent Friedman, Sy-David
n3:wos
000342334000006
s:issn
0016-2736
s:numberOfPages
17
n15:doi
10.4064/fm226-3-6
n16:organizacniJednotka
11210