Zero sharp and Kunen inconsistence.

Asked Jan 31 '14 at 07:34

Active Jan 31 '14 at 07:34

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There is some (deep/shallow/interesting/trivial) relation between:

(1) $\exists 0^\sharp$ iff $\exists j:L\longrightarrow L$ nontrivial elementary embedding.

(2) The Kunen inconsistency $\not\exists j:V\longrightarrow V$ nontrivial elementary embedding.

asked Jan 31 '14 at 07:34

The embedding is not definable in $L$. And that is why $V\neq L$ if $0^#$ exists, and in a very acute way too. – Asaf Karagila Jan 31 '14 at 09:37
Thanks. Some reference about "is not definable"? – Martín-Blas Pérez Pinilla Jan 31 '14 at 09:44
Well... Kunen's theorem, for one. :-) – Asaf Karagila Jan 31 '14 at 09:45
(1) and (2) are Kunen's theorems... Is relevant this: http://math.stackexchange.com/questions/39956/when-does-v-l-becomes-inconsistent? – Martín-Blas Pérez Pinilla Jan 31 '14 at 09:54
I meant the second, of course. – Asaf Karagila Jan 31 '14 at 17:11

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