Explicit algebraic models for constructive and classical theories with non-standard elements

Studia Logica 55 (1):33 - 61 (1995)
We describe an explicit construction of algebraic models for theories with non-standard elements either with classical or constructive logic. The corresponding truthvalue algebra in our construction is a complete algebra of subsets of some concrete decidable set. This way we get a quite finitistic notion of true which reflects a notion of the deducibility of a given theory. It enables us to useconstructive, proof-theoretical methods for theories with non-standard elements. It is especially useful in the case of theories with constructive logic where algorithmic properties are essential.
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