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Constructing Boolean algebras for cardinal invariants

1997/12/15 by Saharon Shelah, Shelah, Saharon
Computer Science · Mathematics · #03E04 #03E05 #03E10 #03G05 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Rings, Modules, and Algebras #math.GN #math.LO #msc:03E04 #msc:03E05 #msc:03E10 #msc:03G05

paper · pdf · doi:10.48550/arxiv.math/9712286

published as Algebra Universalis 45 No. 4 (2001) 353--373

openalex publication_date 1997/12/15 · arxiv created 2000/09/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct Boolean Algebras answering questions of Monk on cardinal invariants. The results are proved in ZFC (rather than giving consistency results). We deal with the existence of superatomic Boolean Algebras with ``few automorphisms'', with entangled sequences of linear orders, and with semi-ZFC examples of the non-attainment of the spread (and hL, hd).

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