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The aim of this note is to find all continuous everywhere defined solutions of the Babbage functional equation stating that the n-th iteration of a function is the identity function.
24 December 2014 /Corrected 29 July 2015

Babbage functional equation

Un survol de la gamme pythagoricienne et une étude, en appendice, de quelques problèmes mathématiques qui en surgissent. À la fin, quelques mots sur la relation entre cette gamme et le Timée de Platon.

Gamme Pythagoricienne

Traduction à l’espagnol par Gonzalo Reyes de la pièce «Lors du deuxième Big Bang»

En el segundo Big Bang


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Version libre d’un article de Jose Ortega y Gasset

Notes d’un été vagabond

 


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Cette version de l’article de Ortega est mise à la disposition du public selon les termes de la licence Creative Commons Paternité – Pas d’Utilisation Commerciale – Pas de Modification 3.0 Unported.
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Published in Volume 6 (Sets and extensions in the 20th Century), North Holland, 2012, of the series “Handbook of History of Logic” edited by Dov M. Gabbay, King’s College London, UK, Akihiro Kanamori and John Woods, University of British Columbia, Vancouver, Canada,

History of Categorical Logic 1963-1977. Jean-Pierre Marquis and Gonzalo E. Reyes

A derivation of Einstein’s vacuum field equations

Preliminary version

General Relativity: Affine connections, parallel transport and sprays

G.E. Reyes, Embedding manifolds with boundary in smooth toposes, Cahiers de Top. et Geom. Diff. Catég., (48), 83-103, (2007). We embed fully and faithfully the category of manifolds with boundary in some “smooth” toposes. We show that the embedding preserves open coverings and some products. Furthermore, it sends a Weil’s prolongation of a manifold by a Weil algebra into the embedded manifold raised to the associated infinitesimal space of the algebra. Our main tool is to “double” the manifold with boundary to obtain one without boundary.

Reyes G.E. A model of SDG in which only trivial distributions with compact support have a density. The aim of this note is to show that in the classifier of the theory of real analytic (i.e. C ω-)rings, linear functionals defined on the exponential whose base is the ring of “reals” (i.e., the generic model) and whose exponent is a finite power of this ring and having values in the reals, are trivial in a sense to be specified, provided that they have a density. This was conjectured by Anders Kock.

A model of SDG in which only trivial distributions with compact support have a density

Preliminary version

Metrics, connections and curvature