Automorphisms of \mathscrP(λ)/\mathscrI_κ

2015/06/10 by Paul Larson, Larson, Paul, Paul McKenney +1
Computer Science · Mathematics · #03E35 #Advanced Algebra and Geometry #Advanced Algebra and Logic #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03E35

paper · pdf · doi:10.48550/arxiv.1506.03433

23 pages

openalex publication_date 2015/06/10 · arxiv created 2015/08/27 · arxiv updated 2015/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study conditions on automorphisms of Boolean algebras of the form P(λ)/I_κ (where λ is an uncountable cardinal and I_κ is the ideal of sets of cardinality less than κ) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every cardinality-preserving automorphism of P(2^κ)/I_κ⁺ which is trivial on all sets of cardinality κ⁺ is trivial, and that MA_ℵ1 implies that every automorphism of P(ℝ)/Fin is trivial on a cocountable set.

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