my questions are:
set with n equals or under 100 and infinite domain
- the set A is recursively enumerable?
- the set A is recursive?
- the set A is semantically closed?
- the complementary set ( $ \overline{A} $ ) is recursively enumerable ?
My try: since n is bounded I should be able to compute this function. So the function belong to the set $R$ (recursive) and $RE$ (Recursively enumerable). But I have some dubs about the infinite domain of function $ {\displaystyle \varphi } $ because maybe this could make my set non-computable.
I'm sorry for my bad grammar as I'm not a native English speaker but I would appreciate any advice for help me to solve this problem.
Thanks a lot