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Disjointness conditions for free products of $$\ell$$-groups. (English) Zbl 0578.06012
This paper considers the cardinality of disjoint sets in free products of $$\ell$$-groups and vector lattices. For abelian $$\ell$$-groups and vector lattices it is shown that free products can have arbitrarily large disjoint sets even when the free factors are totally ordered. In the case of nonabelian varieties of $$\ell$$-groups a proof is given of the fact that free products can have a disjoint set of cardinality $${\mathfrak m}$$ regardless of whether or not the free factors have such a set whenever $${\mathfrak m}$$ is a countable, a singular, or a regular but not weakly compact cardinal.

##### MSC:
 06F15 Ordered groups 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 03E55 Large cardinals
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