A theory with a recursive set of axioms that can derive all its theorems through logical deduction. This property is…
A provability predicate, often denoted as 'Bew', is a fundamental concept in formal logic. It allows us to express within…
A metatheorem is a theorem that describes properties of a formal system, such as consistency or completeness. It operates on…
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…
Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that any consistent system powerful enough for arithmetic will…
Gödel's second incompleteness theorem states that no consistent formal system strong enough to include basic arithmetic can prove its own…
A theory is finitely axiomatizable if it can be completely defined by a finite collection of fundamental statements or axioms.…
Completeness in logic refers to a system's ability to derive every logically valid formula. It ensures that all truths provable…
A provability predicate is a mathematical function that determines whether a statement is provable within a given formal system. It's…