Consistency Strength of the Axiom of Full Reflection at Large Cardinals

Details Consistency Strength of the Axiom of Full Reflection at Large Cardinals Consistency Strength of the Axiom of Full Reflection at Large Cardinals

1994-04-21

arxiv.org/abs/math/9404205v1

Mathematics

Logic

Scientific paper

The Axiom of Full Reflection at a measurable cardinal has been conjectured to be equiconsitent with the existence of a coherent sequence of measures with a repeat point. However we prove that the Axiom of Full Reflection at a measurable cardinal is surprisingly equiconsistent just with the existence of a measurable cardinal. We also generalize the result to larger cardinals as strong or supercompact. Hence we can conclude that the Axiom of Full Reflection at large cardinals weaker than measurable, e.g. as n-Mahlo, does push the consistency strength up, but does not push the consistency strength up at measurable or larger cardinals.

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