Strong induction strengthens the inductive hypothesis, allowing the assumption that the proposition holds for all smaller cases. This powerful technique…
A fundamental theorem in first-order logic. It asserts that if a theory has an infinite model, it possesses models for…
Sequent calculus is a formal system for logical entailments, representing deductions as sequences of formulas. It emphasizes structural rules, providing…
Sequent calculus is a formal system representing logical deductions. It uses sequences of formulas before and after a turnstile, signifying…
A sequence is an ordered list of objects, identified by position. It's fundamental in mathematics for defining functions, sets, and…
A semi-decidable theory allows for an algorithm to list all its theorems. However, it may not offer a way to…
Robinson arithmetic is a simplified version of Peano arithmetic, omitting the induction axiom schema. It provides a weaker yet still…
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.…
Recursive function theory explores the properties of recursive functions, focusing on their computability and classification within complexity hierarchies. It's fundamental…