Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

Epireflections and supercompact cardinals

We prove that, under suitable assumptions on a category C, the existence of supercompact cardinals implies that every absolute epireflective class of objects of C is a small-orthogonality class. More precisely, if L is a localization functor on an accessible category C such that the unit morphism X→LX is an extremal epimorphism for all X, and the class of L-local objects is defined by an absolute formula with parameters, then the existence of a supercompact cardinal above the cardinalities of the parameters implies that L is a localization with respect to some set of morphisms.

Sobre la violencia, Hannah Arendt, Àngela Lorena Fuster (trad.), Gerard Rosich (trad.), Fina Birulés (pròl.)

Motivada por el surgimiento de la reivindicación de la función de la violencia enla política, tanto en el terreno de la acción como en el discurso teórico, en Sobrela violència Arendt interroga la relación entre violencia y poder, entre política ydominación. Tal como señala Fina Birulés en el prólogo, sus reflexiones son elresultado del esfuerzo renovado por comprender las experiencias políticas a lasque Arendt se vio confrontada, en particular, la aparición en la escena pública deun discurso que reivindicaba la violencia como elemento central de la prácticarevolucionaria. Y como en otras ocasiones, la reflexión sobre el presente da lugara la crítica de la tradición de la filosofía política. En este sentido, y de modoejemplar, el libro se constituye como un “ejercicio de pensamiento político” que ala vez que interpreta los acontecimientos interroga las categorías con las que latradición ha pensado la política.