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Generally, number theoretic conjectures which are well-known and easy to explain are either obviously $\Pi^0_1$ or $\Pi^0_2$, which is to say, their truth can be decided by a single membership query ...

This is a very abstract question, I hope this is appropriate. Suppose $T$ is some claim over some infinite set $A$, for example, let $A$ be the set of all loopless planar graphs, and $T$ be the claim "...

Hello. I am currently searching for some nice examples of proofs by induction in the finite case, that can be generalized to the infinite case using transfinite induction (and dont become trivial ...