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Logical Theorem

A logical theorem is a statement proven true within a formal system. It relies on axioms and inference rules, representing…

2 weeks ago

Löb’s Theorem

Löb's theorem in mathematical logic states that if a system can prove that a statement implies its own provability, then…

2 weeks ago

Limitation Result

A limitation result defines the boundaries of what can be achieved in a logical or mathematical system. It often signifies…

2 weeks ago

I-proposition in Traditional Logic

An I-proposition, in traditional logic, is a particular affirmative categorical statement. It asserts that at least some members of the…

2 weeks ago

Introduction Rule in Logic

An introduction rule in logic defines how to logically infer a connective within a proof. It's a fundamental concept in…

2 weeks ago

Interpretation in Formal Languages

Interpretation assigns meaning to symbols and expressions in a formal language. It defines how a specific set of terms is…

2 weeks ago

Independence Results in Logic and Mathematics

An independence result demonstrates that a statement is neither provable nor disprovable within a specific axiomatic system, assuming the system's…

2 weeks ago

Understanding Inconsistency in Logic and Systems

Inconsistency arises when a system contains contradictory elements, making it impossible for all statements to be true simultaneously. This fundamental…

2 weeks ago

Henkin Sentence

A Henkin sentence is a self-referential statement that asserts its own provability within a formal system. It's a foundational concept…

2 weeks ago

Gödel Sentence

A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…

2 weeks ago