Totuusjoukko
Totuusjoukko, translated as “truth set”, is a term used in mathematical logic to describe the collection of interpretations or assignments that make a given logical formula true in a fixed structure or model. In this sense, it captures the semantic meaning of a formula as a relation on the domain of discourse.
In propositional logic, the truth set of a formula φ with respect to a valuation is the set
In first-order logic, a formula φ(x1, ..., xn) with free variables defines a relation on the domain.
The concept is sensitive to the chosen model: the same syntactic formula can have different truth sets
Applications of truth sets appear across model theory, definability theory, and database semantics, where a formula’s