Easton’s theorem and large cardinals

Annals of Pure and Applied Logic 154 (3):191-208 (2008)

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Abstract
The continuum function αmaps to2α on regular cardinals is known to have great freedom. Let us say that F is an Easton function iff for regular cardinals α and β, image and α<β→F≤F. The classic example of an Easton function is the continuum function αmaps to2α on regular cardinals. If GCH holds then any Easton function is the continuum function on regular cardinals of some cofinality-preserving extension V[G]; we say that F is realised in V[G]. However if we also wish to preserve measurable cardinals, new restrictions must be put on F. We say that κ is F-hypermeasurable iff there is an elementary embedding j:V→M with critical point κ such that H)Vsubset of or equal toM; j will be called a witnessing embedding. We will show that if GCH holds then for any Easton function F there is a cofinality-preserving generic extension V[G] such that if κ, closed under F, is F-hypermeasurable in V and there is a witnessing embedding j such that j≥F, then κ will remain measurable in V[G]
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DOI 10.1016/j.apal.2008.02.001
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References found in this work BETA

Powers of Regular Cardinals.William B. Easton - 1970 - Annals of Mathematical Logic 1 (2):139-178.
The Negation of the Singular Cardinal Hypothesis From o=K++.Moti Gitik - 1989 - Annals of Pure and Applied Logic 43 (3):209-234.
Perfect Trees and Elementary Embeddings.Sy-David Friedman & Katherine Thompson - 2008 - Journal of Symbolic Logic 73 (3):906-918.
Perfect-Set Forcing for Uncountable Cardinals.Akihiro Kanamori - 1980 - Annals of Mathematical Logic 19 (1-2):97-114.

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Citations of this work BETA

Fusion and Large Cardinal Preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.
Fusion and Large Cardinal Preservation.Sy-David Friedman, Radek Honzik & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (12):1247-1273.
Global Singularization and the Failure of SCH.Radek Honzik - 2010 - Annals of Pure and Applied Logic 161 (7):895-915.
The Failure of GCH at a Degree of Supercompactness.Brent Cody - 2012 - Mathematical Logic Quarterly 58 (1):83-94.
Eastonʼs Theorem and Large Cardinals From the Optimal Hypothesis.Sy-David Friedman & Radek Honzik - 2012 - Annals of Pure and Applied Logic 163 (12):1738-1747.

View all 7 citations / Add more citations

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