Large Cardinals and the Continuum Hypothesis

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11210%2F13%3A10173337" target="_blank" >RIV/00216208:11210/13:10173337 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Large Cardinals and the Continuum Hypothesis

Original language description

This is a survey paper which discusses the impact of large cardinals on provability of the Continuum Hypothesis (CH). It was Gödel who first suggested that perhaps "strong axioms of infinity" (large cardinals) could decide interesting set-theoretical statements independent over ZFC, such as CH. This hope proved largely unfounded for CH - one can show that virtually all large cardinals defined so far do not affect the status of CH. It seems to be an inherent feature of large cardinals that they do not determine properties of sets low in the cumulative hierarchy if such properties can be forced to hold or fail by small forcings.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2013

Confidentiality

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

Name of the periodical

Acta Universitatis Carolinae. Philosophica et Historica

ISSN

0567-8293

e-ISSN

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Volume of the periodical

2010

Issue of the periodical within the volume

2

Country of publishing house

CZ - CZECH REPUBLIC

Number of pages

17

Pages from-to

35-52

UT code for WoS article

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EID of the result in the Scopus database

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