Soundness ensures that a logical system's derived theorems are always true under any interpretation. It's a fundamental property for reliable…
An open term is an expression in a formal language with free variables. It doesn't represent a specific object or…
An open formula in a formal language is an expression with unbound variables. Its truth value depends on the specific…
Explore infinitary concepts, dealing with expressions of infinite length in logic, languages, and operations. Essential for advanced theoretical computer science…
A self-referential sentence in formal systems, a Gödel sentence demonstrates incompleteness theorems by asserting its own unprovability within that system.…
Formation rules define the syntax of a formal language, dictating how basic symbols combine to create valid, well-formed formulas. These…
A crucial lemma in Gödel's incompleteness theorems. It states that for any formula with one free variable, there exists a…
Church's theorem proves the undecidability of fundamental decision problems in logic, like the Entscheidungsproblem. It demonstrates that no logic can…
A provability predicate is a mathematical function that determines whether a statement is provable within a given formal system. It's…