Henkin's completeness proof for FOL depends on the homogeneity of the domain, and many-sorted domains introduce partition constraints that can block canonical model construction for infinite sort hierarchies.

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Canonical model construction(the technique that may fail when dealing with infinite sort hierarchies): A standard method for building an example or 'model' that satisfies all the rules of a logical system—it's a way of proving a system actually works.
Completeness proof(as a key concept in logic): A mathematical argument showing that a logical system is 'complete'—that is, if something is true, there's a way to prove it using the system's rules.
First-order logic (FOL)(the logical system being discussed): A formal system for reasoning where you can make statements about objects and their properties, but you can't directly make claims about claims themselves—it's the most common 'language' logicians use to study reasoning.
Henkin: # Henkin Henkin refers to Leon Henkin, a 20th-century American logician and mathematician who made important contributions to mathematical logic and the foundations of mathematics. He is most famous for developing "Henkin models," a technique that helps prove certain mathematical statements are possible by constructing concrete examples that satisfy specific logical rules. His work made complex abstract logic more accessible and practical for mathematicians and philosophers studying what can and cannot be proven in formal systems.

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