AUC PHILOSOPHICA ET HISTORICA
AUC PHILOSOPHICA ET HISTORICA

AUC Philosophica et Historica (Acta Universitatis Carolinae Philosophica et Historica) is a multidisciplinary academic journal focused on the humanities with more than 50 years of tradition.

The journal is indexed in CEEOL, DOAJ, and EBSCO.

AUC PHILOSOPHICA ET HISTORICA, Vol 2010 No 2 (2010), 35–52

Large Cardinals and the Continuum Hypothesis

Radek Honzík

published online: 18. 05. 2015

abstract

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. The paper can also be used as an introductory text on large cardinals as it de_nes all relevant concepts.

keywords: large cardinals; forcing


periodicity: 2 x per year
ISSN: 0567-8293
E-ISSN: 2464-7055

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