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Classification of Finite Spaces of Orderings

Published online by Cambridge University Press:  20 November 2018

Murray Marshall
Murray Marshall*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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1. Introduction. A space of orderings will refer to what was called a “set of quasi-orderings” in [5]. That is, a space of orderings is a pair (X, G) where G is an elementary 2-group (i.e. x2 = 1 for all x ∈ G) with a distinguished element – 1 ∈ G, and X is a subset of the character group x(G) = Horn (G, {1, –1};) satisfying the following properties:

01: X is a closed subset of χ(G).

02: σ(−l) = −1 holds for all σ ∊ X.

03: X⊥ = {a ∊ G|χa = 1 for all a ∊ X} = 1.

04: If f and g are forms over G and if x ∊ Df⊗g, then there exist y ∊ Df and z ∊ Dg such that x ∊ D(y, z).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 320 - 330
Copyright
Copyright © Canadian Mathematical Society 1979

References

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