We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive types exist in any Martin-L¨of categ...
In our previous work [17] we have shown that for any ω-algebraic meet-cpo D, if all higher-order stable function spaces built from D are ω-algebraic, then D is finitary. This ac...
: Countably based filter spaces have been suggested in the 1970's as a model for recursion theory on higher types. Weak limit spaces with a countable base are known to be the ...
Sierpinski space is injective in the category Top of topological spaces, but not in any of the larger cartesian closed categories Conv of convergence spaces and Equ of equilogica...
Lax logical relations are a categorical generalisation of logical relations; though they preserve product types, they need not preserve exponential types. But, like logical relatio...
Gordon D. Plotkin, John Power, Donald Sannella, Ro...