Higher-Order Variables in Logic
A higher-order variable represents functions, predicates, or relations, distinguishing it from variables…
Gödel’s Second Incompleteness Theorem
Gödel's second incompleteness theorem states that no consistent formal system strong enough…
Gödel’s First Incompleteness Theorem
Gödel's First Incompleteness Theorem states that any consistent formal system capable of…
Gödel Sentence
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems…
First-Order Theory
A first-order theory formalizes mathematical reasoning using first-order logic. It defines relationships…
Finitely Axiomatizable Theories
A theory is finitely axiomatizable if it can be completely defined by…
Finite Character: Understanding Limited Systems
Finite character describes systems where all essential properties can be understood by…