A logical theorem is a statement proven true within a formal system. It relies on axioms and inference rules, representing…
Löb's theorem in mathematical logic states that if a system can prove that a statement implies its own provability, then…
A limitation result defines the boundaries of what can be achieved in a logical or mathematical system. It often signifies…
An I-proposition, in traditional logic, is a particular affirmative categorical statement. It asserts that at least some members of the…
An introduction rule in logic defines how to logically infer a connective within a proof. It's a fundamental concept in…
Interpretation assigns meaning to symbols and expressions in a formal language. It defines how a specific set of terms is…
An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…
Inconsistency arises when a system contains contradictory elements, making it impossible for all statements to be true simultaneously. This fundamental…
A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…