Special groups whose isometry relation is a finite union of cosets

0-stable 0-categorical linked quaternionic mappings are studied and are shown to correspond (in some sense) to special groups which are 0stable, 0-categorical, satisfy AP(3) and have finite 2-symbol length. They are also related to special groups whose isometry relation is a finite union of cosets, which are then considered on their own, as well as their links with pseudofinite, profinite and weakly normal special groups. The algebraic theory of quadratic forms is naturally divided into the reduced theory of quadratic forms (corresponding to the theory of quadratic forms over formally real Pythagorean fields) and the non-(necessarily) reduced theory. The former, with its links with the theory of orderings is much more developed, and a striking example of this is Marshall's classification of spaces of orderings of finite chain length ([20]). In the language of other axiomatisations of the algebraic theory of quadratic forms, it tells us that Witt rings, or special groups, or linked...

• Type: Journal
• Year: 2008
• Where: JSYML
• Authors: Vincent Astier
• Keywords: JSYML 2008, Quadratic Forms, Quaternionic Mappings, Special Groups