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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.

19 votes
6 answers
2k views

Complete mathematics

Hello, I would like to ask you if there is a mathematical theory, that is complete (in the sense of Goedel's theorem) but practically applicable. I know about Robinson arithmetic that is very limited …
1 vote
1 answer
668 views

FOL->ZF->HOL (Interpretation)

Hello. This may not count as a research question, but I guess it's too much for math.stackexchange. Could we define ZF (Zermelo-Fraenkel Set theory) in classical first-order predicate calculus, then …