Provability logic, a subset of modal logic, explores the formal properties of provability. It uses modal operators to express concepts…
Monadic first-order logic simplifies first-order logic by using only predicates with a single argument. This focuses on the properties of…
Metalogic explores the inherent properties of formal logical systems and languages. It investigates crucial aspects such as consistency, completeness, and…
Löb's theorem in mathematical logic states that if a system can prove that a statement implies its own provability, then…
Löb's paradox, a puzzle in modal logic, questions the formalization of provability within a system. It leads to counterintuitive results…
A limitation result defines the boundaries of what can be achieved in a logical or mathematical system. It often signifies…
Explore Stephen Cole Kleene's three-valued logic system, K3. It introduces an 'undefined' truth value alongside true and false, offering a…
Mathematics built on intuitionistic logic, prioritizing constructive proofs and avoiding non-constructive axioms like the law of excluded middle. It emphasizes…
Intuitionism is a philosophy of mathematics that questions the existence of the mathematical infinite and the completeness of mathematical truth.…
Explore infinitary concepts, dealing with expressions of infinite length in logic, languages, and operations. Essential for advanced theoretical computer science…