6

The answer is no, one can have models of ZFC set theory with a definable truth predicate for first-order truth in $L$, but without having $0^\sharp$.
One way to build such a model is like this. In Kelly-Morse KM set theory, you can prove the existence of a truth predicate for first-order truth for the whole universe $V$, and then by forcing you can code ...

answered Jun 6 '13 at 22:19

Joel David Hamkins

183k2828 gold badges545545 silver badges951951 bronze badges

2

Well assuming that $\lambda^A$ is always the first recursively admissible which is bigger than $\omega_1^A$, which I think should be true, I think my question is after all not so interesting:
Either there is a largest recursively inaccessible smaller than $\omega_1^A$, in which case $\lambda^A$ is a successor in the recursively inaccessible ordinals, or $\...

Only top voted, non community-wiki answers of a minimum length are eligible

#### Related Tags

infinite-time-computability × 4set-theory × 3

lo.logic × 1

computability-theory × 1

mathematical-philosophy × 1

constructive-mathematics × 1

ordinal-numbers × 1

inner-model-theory × 1

intuitionism × 1