Some properties of local partial clones on an infinite set

We investigate the interpolation and extrapolation properties of partial clones of infinite-valued logic functions. A maximal local partial clone on an infinite set E is characterized by conditions on its intersections with the full partial clone on every finite subset A⊂E, 2≤/A /<∞. Next, the criterion is given for a finite domain partial operation of a local partial clone to be extendable to the everywhere defined operation from the same clone. A similar criterion is also given for a local partial clone to be extendable. Finally, extendibility conditions for partial orders are obtained so that the clones of their partial n-endomorphisms become extendable.