 
Summary: Fully Complete Minimal PER Models for the
Simply Typed calculus ?
Samson Abramsky 1 and Marina Lenisa 2
1 Oxford University Computing Laboratory
Wolfson Building, Parks Road, OX1 3QD, England.
email: Samson.Abramsky@comlab.ox.ac.uk
2 Dipartimento di Matematica e Informatica, Universita di Udine,
Via delle Scienze 206, 33100 Udine, ITALY.
email: lenisa@dimi.uniud.it.
Abstract. We show how to build a fully complete model for the maximal
theory of the simply typed calculus with k ground constants, k . This
is obtained by linear realizability over an aĆne combinatory algebra of
partial involutions from natural numbers into natural numbers. For sim
plicitly, we give the details of the construction of a fully complete model
for k extended with ground permutations. The fully complete minimal
model for k can be obtained by carrying out the previous construction
over a suitable subalgebra of partial involutions. The full completeness
result is then put to use in order to prove some simple results on the
maximal theory.
Introduction
