Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege,
The … See more

Structural proof theory is the subdiscipline of proof theory that studies the specifics of proof calculi. The three most well-known styles of proof calculi are:
• The Hilbert calculi
• The natural deduction calculi… See more

Ordinal analysis is a powerful technique for providing combinatorial consistency proofs for subsystems of arithmetic, analysis, and set theory. Gödel's second incompleteness theorem is often interpreted as demonstrati… See more

Provability logic is a modal logic, in which the box operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory. As basic axioms of the provability l… See more

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The field was founded by Harvey Friedman. Its defining method ca… See more

Functional interpretations are interpretations of non-constructive theories in functional ones. Functional interpretations usually proceed in two stages. First, one "reduces" a classical theory C to … See more