All Questions

The arithmetic hierarchy is naturally extended to all ordinals via ordinal notations creating a hierarchy for all hyperarithmetic sets. The polynomial time hierarchy is defined analogously to the ...

Does there exist a function $f$ that satisfies all of the following three properties? The function converts an arbitrarily large (empty, finite, countably/uncountably infinite) set of ordinals to a ...

Gostanian's paper "The next admissible ordinal" (see https://www.sciencedirect.com/science/article/pii/0003484379900251 ), is concerned with the supremum of the $\alpha$-recursive ordinals for various ...

It's known, for example in the answer to this question: Is there a computable model of ZFC? that ZFC has no computable model. My questions is: is there a model of ZFC for which the order relation on ...

Consider the following statement (which follows easily from various results found in the literature): (†) There exists a primitive recursive (“p.r.”) relation $T$ on the ordinals such that, if $(...