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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
0
votes
Can transfinite induction be defined as axiom scheme in FOL on bin-tree structures?
Assuming I understand your comment right, I don't know that binary trees are enough to get there, but arbitrary finite trees should certainly be. One natural induction-esque principle on trees would …
18
votes
Accepted
Why don't Zeilberger and Gosper's algorithms contradict Richardson's theorem?
(Comment turned into an answer:)
It's as simple as "the composition of hypergeometric terms is not hypergeometric". $f(n)=2^n$ is a hypergeometric term because $\frac{f(n+1)}{f(n)}=2$ is a rational te …