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Classification of Finite Spaces of Orderings

Published online by Cambridge University Press:  20 November 2018

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 xG) 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 σX.

03: X⊥ = {aGa = 1 for all aX} = 1.

04: If f and g are forms over G and if xDfg, then there exist yDf and zDg such that xD(y, z).

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1979

References

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