A weak counterexample in intuitionistic logic signifies a lack of positive evidence for an instance of the law of excluded…
Topos theory studies categories resembling the category of sets, forming a foundation for mathematics. It enables generalized concepts of computation…
A strong counterexample in intuitionistic logic disproves an instance of the law of excluded middle. It's a proof of negation,…
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.…
An extension of the simple theory of types, the ramified theory introduces levels to distinguish objects and functions by order,…
The philosophy of logic explores the fundamental nature, assumptions, and implications of logical systems. It scrutinizes the very tools we…
Neo-logicism revives the logicist project of grounding mathematics in logic. It addresses criticisms of traditional logicism with new insights and…
Neo-Fregeanism revives Frege's logicist project, aiming to base mathematics on logic. It utilizes Hume's Principle and other axioms to ground…