An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…
Gödel's incompleteness theorems reveal fundamental limits of formal systems. They demonstrate that any consistent system powerful enough for arithmetic will…
The property of a logical or mathematical system where not all true statements can be proven within the system's own…
A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…
Gödel's First Incompleteness Theorem states that any consistent formal system capable of basic arithmetic contains true statements that are unprovable…
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…
Glivenko's theorem in logic connects classical and intuitionistic systems. It states that any formula provable in classical logic is also…
The disjunction property in intuitionistic logic asserts that if a statement P or Q is provable, then either P alone…
A crucial lemma in Gödel's incompleteness theorems. It states that for any formula with one free variable, there exists a…
Two theories are deductively equivalent if they can prove the exact same set of theorems. This means they offer the…