Ueber neue einfache Ultrafilter II

Hippokrates Ueber die Krankheiten III

irrelevant. Chemistry and the relations between science, technology, and industry are well surveyed by Crosland and Cardwell respectively. Forbes's essay on mathematical cosmography is not a comprehensive account but the story (albeit interesting) of a few German cartographers. Compared with other recent collections of essays in the history of science, this volume parades no party line: witness...

Ultrafilter Extensions for Coalgebras

This paper studies finitary modal logics as specification languages for Set-coalgebras (coalgebras on the category of sets) using Stone duality. It is wellknown that Set-coalgebras are not semantically adequate for finitary modal logics in the sense that bisimilarity does not in general coincide with logical equivalence. Stone-coalgebras (coalgebras over the category of Stone spaces), on the ot...

The Ultrafilter Closure in ZF

It is well known that, in a topological space, the open sets can be characterized using filter convergence. In ZF (Zermelo-Fraenkel set theory without the Axiom of Choice), we cannot replace filters by ultrafilters. It is proven that the ultrafilter convergence determines the open sets for every topological space if and only if the Ultrafilter Theorem holds. More, we can also prove that the Ult...

Neue Funktionen

Ueber Das Verschwinden Der Θ-functionen