Remarks on isomorphisms in typed lambda calculi with empty and sum types. (English summary) Ann. Pure Appl. Logic 141 (2006), no. 1-2, 35–50. This paper, as the title suggests, studies isomorphisms in typed lambda calculi with empty and sum types. For types built out of the well-behaved type constructors: unit, product and arrow, the following hold: (1) Two types are isomorphic if their associated arithmetic expressions are equal in the standard model of natural numbers. (2) Type isomorphism is finitely axiomatisable and decidable. This paper shows that (1) and (2) fail when the empty and sum type constructors are involved. In particular, the paper shows that: • Property (1) fails in the presence of arrow, empty and sum types and in this case type isomorphism and axiomatic equality do not coincide. • Property (2) fails in the presence of product, arrow and sum type constructors and in this case type isomorphism is not finitely axiomatisable
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