Foundational concepts underlying how mathematics itself is built and reasoned about: axioms, formal systems, proof, and the theory of sets and infinite collections. Belongs here: Axiom, Boolean Algebra, Cantor's Diagonal Argument, Cardinality, Countable Set, Formal System, Infinity, Mathematical Proof and Sets. Does not belong here: a concept from a specific branch that merely uses logic or sets as a tool, such as a Group or a Manifold.