Uniform
spaces can be Cauchy-completed; and if the base space was a
first-order structure, this structure can be naturally extended to
the completion. While common in algebra, this construction has
been more recently used to produce new models of special set
theories. We investigate here a natural way to ``twist'' the
semantics of any structure according to a uniformity on its
universe. We use it to relate the (classical first-order) theories
of structures and dense substructures and apply it to the case of
Cauchy-completions.
Publié le : 2004-03-14
Classification:
formula balancing,
uniform model theory,
uniformly continuous valuation,
03C30,
54E15,
03G30
@article{1080056164,
author = {Rigo, Armin},
title = {Formula balancing and continuously valuated models},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {11},
number = {1},
year = {2004},
pages = { 111-125},
language = {en},
url = {http://dml.mathdoc.fr/item/1080056164}
}
Rigo, Armin. Formula balancing and continuously valuated models. Bull. Belg. Math. Soc. Simon Stevin, Tome 11 (2004) no. 1, pp. 111-125. http://gdmltest.u-ga.fr/item/1080056164/