Reverse mathematics investigates the logical strength of mathematical theorems. It aims to identify the minimal axiomatic systems required to prove…
A relative consistency proof demonstrates that if a system S is consistent, adding new axioms to S also maintains consistency.…
A theory with a recursive set of axioms that can derive all its theorems through logical deduction. This property is…
An extension of the simple theory of types, the ramified theory introduces levels to distinguish objects and functions by order,…
Pure first-order logic is a foundational system in logic, characterized by its exclusion of function symbols and identity. It relies…
Provability logic, a subset of modal logic, explores the formal properties of provability. It uses modal operators to express concepts…
Proof-theoretic consequence, also known as syntactic consequence, explores logical entailment based on the structure of proofs within formal systems. It…
Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning,…
A primitive recursive relation is a type of relation definable using primitive recursive functions. These relations represent a subset of…
Primitive recursive functions are a subset of computable functions defined using initial functions and operations like composition and primitive recursion.…