Delta0definable
Delta0definable, often written Δ₀, refers to a class of formulas and sets in mathematical logic and arithmetic that use only bounded quantifiers. A formula is Δ₀-definable if every quantifier appearing in it is of the form ∀x < t or ∃x < t, where the bound term t is a numerically defined expression. This restriction ensures that the formula cannot express unbounded recursion or global properties that would require quantification over arbitrarily large numbers.
In the arithmetical hierarchy, Δ₀ formulas coincide with both Σ₀ and Π₀ sets. They are the simplest nontrivial class
Delta0definable formulas are central to the study of formal systems such as Peano arithmetic. Induction over Δ₀
Delta0definable sets are closed under Boolean operations and substitution, making them a robust foundation for constructing