Pure First-Order Logic
Pure first-order logic is a foundational system in logic, characterized by its…
Non-Standard Models in Logic and Mathematics
A non-standard model adheres to a theory's axioms but possesses unintended properties.…
Metamathematics
Metamathematics examines mathematical systems and theories from an elevated viewpoint, employing principles…
Gödel’s Incompleteness Theorems
Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that…
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…
Frege’s Theorem
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how…