Atsuji completions: Equivalent characterisations

Characterisations of Morita equivalent inverse semigroups

For a fixed inverse semigroup S, there are two natural categories of left actions of S: the category Fact of unitary actions of S on sets X meaning actions where SX = X, and the category Étale of étale actions meaning those unitary actions equipped with a function p : X → E(S), to the set of idempotents of S, such that p(x)x = x and p(sx) = ses∗, where s∗ denotes the inverse of s. The category ...

Equivalent martingale measures and optimal market completions

Optimal fictitious completions of an incomplete financial market are shown to be associated with exponential martingales (not just local martingales) and, therefore, to "an optimal equivalent martingale measure'. Results of independent interest, in the theory of continuous-time martingales, are derived as well. iirshurgb, PA 15213-3890

Non-deterministic Characterisations

In this paper, we extend Jones’ result—that cons-free programming with kth-order data and a callby-value strategy characterises EXPTIME—to a more general setting, including pattern-matching and non-deterministic choice. We show that the addition of non-determinism is unexpectedly powerful in the higher-order setting. Nevertheless, we can obtain a non-deterministic parallel to Jones’ hierarchy r...

Geometric Characterisations of Groups

Relative Completions

We compute the completion of the groups SLn(Zt]) and SLn (Zt;t ?1 ]) relative to the obvious homomorphisms to SLn (Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second cohomology of these groups.