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Preliminaries Amalgamations in the Class of Partial Algebras
Amalgamations in the Class of Ordered Sets
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amalgamation of G Amalgamation Property Archimedian o-groups B. H. Neumann Boolean algebras cardinal number Cartesian product class of Abelian class of ordered cofinal cofinal subset convex subgroup Corollary define denote directed subset disjoint divisible Abelian o-groups element of G epimorphism equivalent extends the given free sum Furthermore G and H g e G G in H hence homomorphism implies inclusion map interval of g isomorphism lattice ordered groups Lemma let 9 Let G Let H minimal element mod 9 nonzero interval o-permutation ordered subgroup ordered subset partially ordered set positive element prime subgroup real numbers regular cardinal representing set set of amalgamations similar partial algebras standard amalgamation strong intersection property subgroup of H suppose totally ordered transfinite induction unique valuation of G weak intersection property whence zero interval