About: Easton functions and supercompactness

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Easton functions and supercompactness Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.4064/fm226-3-6
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]. (en)
Title	Easton functions and supercompactness Easton functions and supercompactness (en)
skos:prefLabel	Easton functions and supercompactness Easton functions and supercompactness (en)
skos:notation	RIV/00216208:11210/14:10289626!RIV15-MSM-11210___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Honzík, Radek
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Filozofická fakulta
http://linked.open...dnocenehoVysledku	12834
http://linked.open...ai/riv/idVysledku	RIV/00216208:11210/14:10289626
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Easton's theorem; continuum function; supercompactness (en)
http://linked.open.../riv/klicoveSlovo	Easton's theorem supercompactness continuum function
http://linked.open...odStatuVydavatele	PL - Polská republika
http://linked.open...ontrolniKodProRIV	[1AC7AFDF3C9C]
http://linked.open...i/riv/nazevZdroje	Fundamenta Mathematicae
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	226
http://linked.open...iv/tvurceVysledku	Honzík, Radek Friedman, Sy-David Cody, Brent
http://linked.open...ain/vavai/riv/wos	000342334000006
issn	0016-2736
number of pages	17 (xsd:int)
http://bibframe.org/vocab/doi	10.4064/fm226-3-6
http://localhost/t...ganizacniJednotka	11210

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software