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Parametric models of polymorphic lambda calculus have the structure of enriched categories with cotensors and ends in some generalized sense, and thus have many categorical data types induced by them. The !-order minimum model is a parametric model.
This paper shows the inhabitance in the lambda calculus with negation, product, and existential types is decidable. This is proved by showing existential quantification can be eliminated and reducing the problem to provability in intuitionistic propositional logic. By the same technique, this paper also shows existential quantification followed by negation… (More)
We deene well-partial-orderings on abstract algebras and give their order types. For every ordinal in an initial segment of Bachmann hierarchy there is one and only one (up to isomorphism) algebra giving the ordinal as order type. As a corollary, we show Kruskal-type theorems for various structures are equivalent to well-orderedness of certain ordinals.