Orthogonal basis of a nite dimensional ultrametric semi-normed space ,
Let (K, |.|) be a spherically complete ultrametric valued eld ,
Existence of bases implies the axiom of choice, Axiomatic set theory, vol.31, p.3133, 1983. ,
Some theorems on vector spaces and the axiom of choice, Fund. Math, vol.54, p.95107, 1964. ,
Model theory, of Encyclopedia of Mathematics and its Applications, vol.42, 1993. ,
Consequences of the Axiom of Choice, vol.59, 1998. ,
On vector spaces over specic elds without choice, MLQ Math. Log. Q, vol.59, issue.3, p.128146, 2013. ,
The Hahn-Banach theorem for non-Archimedean valued elds, Proc. Cambridge Philos. Soc, vol.48, p.4145, 1952. ,
The Axiom of Choice, 1973. ,
Reduced powers of the real number system and equivalents of the Hahn-Banach extension theorem, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos, p.123137, 1967. ,
Linear forms and axioms of choice, Comment. Math. Univ. Carolin, vol.50, issue.3, p.421431, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-01186172
Functional analysis and valuation theory, Pure and Applied Mathematics, vol.5, 1971. ,
Nonarchimedean functional analysis, Springer Monographs in Mathematics, 2002. ,
Non-Archimedean functional analysis, volume 51 of Monographs and Textbooks in Pure and Applied Math, 1978. ,
The axiom of choice in p-adic functional analysis, p-adic functional analysis, vol.137, p.151156, 1990. ,
Topological elds, North-Holland Mathematics Studies, vol.157, p.126, 1989. ,
Bâtiment 2, 2 rue Joseph Wetzell, 97490 Sainte Clotilde Email address: Marianne.Morillon@univ-reunion ,