We generalize Warnaar's elliptic extension of a Macdonald multi-parameter summation formula to Riemann surfaces of arbitrary genus. We start by a brief outline of the general theory of hypergeometric type series built from Jacobi theta functions [12, 13] (its extension to integrals [15] is not touched at all). Within this approach univariate elliptic hypergeometric series are defined as the ser...

We present a higher-order calculus ECC which can be seen as an extension of the calculus of constructions CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics may be adequately formalized. It is shown that ECC is strongly normalizing and has other nice proo...

We build a lambda model which characterizes completely (persistently) normalizing, (persistently) head normalizing, and (persistently) weak head normalizing terms. This is proved by using the finitary logical description of the model obtained by defining a suitable intersection type assignment system.

We present a higher-order calculus ECC which can be seen as an extension of the calculus of constructions CH88] by adding strong sum types and a fully cumulative type hierarchy. ECC turns out to be rather expressive so that mathematical theories can be abstractly described and abstract mathematics may be adequately formalized. It is shown that ECC is strongly normalizing and has other nice proo...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.