Henkinmodeller

Henkinmodeller is a software framework and conceptual tool designed to construct Henkin models for first-order theories in mathematical logic. Named after Leon Henkin, it operationalizes the Henkin construction used in the completeness proof by systematically extending a theory with new constants to serve as witnesses for existential statements and by forming a canonical model from the resulting term algebra.

The core idea implemented by Henkinmodeller is to expand the language with Henkin constants and to consider the theory in this expanded language, augmented by sentences asserting relationships between these constants and existing terms. The framework then builds a term model, where elements are equivalence classes of terms under provable equality, and interprets function and relation symbols in a way that satisfies the axioms of the extended theory. This process can be performed iteratively to achieve a saturated view of the model or to illustrate finite approximations of the construction.

Typical features include language management for adding Henkin constants, automated deduction to determine necessary identifications among terms, construction and visualization of the resulting term model, and verification checks that the model satisfies the specified theory or its Henkin extension. Some implementations also provide Skolemization tools, witness extraction for existential statements, and interfaces for educational demonstrations or research experiments.

Henkinmodeller is used primarily in education to illustrate the completeness theorem, in theoretical research to experiment with model construction techniques, and as a teaching aid for demonstrating how existential witnesses lead to concrete models in first-order logic. It complements general theorem provers and model checkers by focusing on the constructive aspects of Henkin models.