Geodesic
An Application of Ultraproducts to Lattice-Ordered Groups
Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1063-1064

Voir la notice de l'article provenant de la source Cambridge University Press

Using ultraproducts, N. R. Reilly proved that if G is a representable lattice-ordered group and J is an independent subset totally ordered by ≺, then the order on G can be extended to a total order which induces ≺ on J (see [5]). In [4], H. A. Hollister proved that a group G admits a total order if and only if it admits a representable order and, moreover, every latticeorder on a group is the intersection of right total orders. The purpose of this paper is to provide a partial converse, viz: if G is a lattice-ordered group and J is an independent subset totally ordered by ≺, then the order on G can be extended to a right total order which induces ≺ on J. 
Glass, A. M. W. An Application of Ultraproducts to Lattice-Ordered Groups. Canadian journal of mathematics, Tome 24 (1972) no. 6, pp. 1063-1064. doi: 10.4153/CJM-1972-108-2
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[1] 1. Chang, C. C. and Keisler, H. J., Model theory (to be published). Google Scholar

[2] 2. Conrad, P. F., Free lattice-ordered groups, J. Algebra, 16 (1970), 191–203. Google Scholar

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[5] 5. Reilly, N. R., Some applications of wreath products and ultraproducts in the theory of lattice ordered groups, Duke Math. J. 36 (1969), 825–834. Google Scholar

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