a little question about admissible sets: Is every $\mathfrak{M}$-admissible ordinals an admissible ordinal ? where $\mathfrak{M}$ is a $L$-structure over $L=\{R_1,\dots,R_k \}$.
Thanks.
a little question about admissible sets: Is every $\mathfrak{M}$-admissible ordinals an admissible ordinal ? where $\mathfrak{M}$ is a $L$-structure over $L=\{R_1,\dots,R_k \}$.
Thanks.
Removing this question from the unanswered list:
Yes, admissibility relativizes downward. For a transitive structure to be admissible, it must be amenable, and satisfy $\Sigma_0$-collection. Both are conditions that keep holding if you "remove parameters". This is obvious for amenability. For collection, a little argument is needed. If you have access to Devlin's "Constructibility" book, this is at the beginning of II.7. (Andres Caicedo)