Adjoining a Strong Unit to an Archimedean Lattice-Ordered Group

摘要

Within archimedean l-groups, "G is an element of SW*" means there are H with strong unit (H is an element of W*) and an embedding G = H. A. Theorem (6.1).ForXa Tychonoff space (or completely regular locale), C(X) is an element of SW*iffXis pseudocompact (which meansC(X) is an element of W*). But any G is an element of SW* embeds into various C(X), and any C(X) contains many H is an element of W*. We define cardinal invariants bG, dG, lambda G which generalize respectively, the bounding and dominating numbers for Double-struck capital RN, and d, and the pi-weight of a topological space. B. Theorem (6.3, 7.5).SupposeG = C(X), andXcontains densely & Union;IXi, theX(i)compact. ThenG is an element of SW*if either (|I| = omega anddG) or (|I|banddG=omega).This "omega,b symmetry" fades a bit in the following, where p is the pseudo-intersection number for Double-struck capital RN (p = b, with = under Martin's Axiom). C. Theorem (8.2).G is an element of SW*if either(dG=omega and lambda Gb) or (dG9) show limits on the hypotheses in B and C.