Reverse mathematics investigates the logical strength of mathematical theorems. It aims to identify the minimal axiomatic systems required to prove…
A predicate P represents a function f if P(x1,...,xn,y) is true iff f(x1,...,xn)=y. A unary predicate P represents set S…
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,…
A provability predicate, often denoted as 'Bew', is a fundamental concept in formal logic. It allows us to express within…
Proof theory is a branch of mathematical logic focused on the structure and properties of mathematical proofs. It formalizes reasoning,…
A theory is Post consistent if it contains at least one unprovable statement. If all statements are provable, the theory…
A formal system of arithmetic using axioms by Giuseppe Peano, it provides a foundational basis for the theory of natural…
Ordered logic is a type of formal logic that prohibits weakening and permutation rules. This ensures that inferences made within…