We propose a new operational model for shared variable concurrency, in the context of a concurrent, higher-order imperative language à la ML. In our model the scheduling of threads is cooperative, and a non-terminating process suspends itself on each recursive call. A property to ensure in such a model is fairness, that is, any thread should yield the scheduler after some finite computation. To...

Realizability interpretations of logics are given by saying what it means for computational objects of some kind to realize logical formulae. The computational objects in question might be drawn from an untyped universe of computation, such as a partial combinatory algebra, or they might be typed objects such as terms of a PCF-style programming language. In some instances, one can show that a p...

Abstract We provide a new forbidden criterion for the realizability of smooth tropical plane curves. This in turn provides us complete classification curves up to genus six.

Given a partial combinatory algebra (pca) A (see e.g. [16]) together with a subpca A# of A we will construct the nested realizability topos RT(A,A#) as described in [5] (without giving it a proper name there). It is well known (from e.g. [16]) that RT(A,A#) appears as the exact/regular completion of its subcategory Asm(A,A#) of assemblies. In [5] the authors considered two complementary subtopo...

The main purpose of this paper is to take apart the reducibility method in order to understand how its pieces fit together, and in particular, to recast the conditions on candidates of reducibility as sheaf conditions. there has been a feeling among experts on this subject that it should be possible to present the reducibility method using more semantic means, and that a deeper understanding wo...