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Inductive Set Definition

Definition: An inductive definition of a set S is a collection of formulas

(forall x₁,...,x_m₁, y₁ in S, ..., y_n₁ in S:

f₁(x₁, ..., x_m₁, y₁, ..., y_n₁) in S)

, ... ,

(forall x₁,...,x_{m_c}, y₁ in S, ..., y_{n_c} in S:

f_c(x₁, ..., x_{m_c}, y₁, ..., y_{n_c}) in S)

where we call the function constants f₁, ..., f_c the constructors of S.

Author: Wolfgang Schreiner
Last Modification: November 24, 1999