Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type theory.

This tag is concerned with questions about interpretability of mathematical entities in various foundational systems, exposing the merits and limits of those systems in achieving that interpretation.