Automorphisms of $\left(\lambda \right)/{ℐ}_{\kappa }$

@article{PaulLarson2016,
abstract = {We study conditions on automorphisms of Boolean algebras of the form $(λ)/ℐ_\{κ\}$ (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 automorphism of $(2^\{κ\})/ℐ_\{κ⁺\}$ which is trivial on all sets of cardinality κ⁺ is trivial, and that $MA_\{ℵ₁\}$ implies both that every automorphism of (ℝ)/Fin is trivial on a cocountable set and that every automorphism of (ℝ)/Ctble is trivial.},
author = {Paul Larson, Paul McKenney},
journal = {Fundamenta Mathematicae},
keywords = {automorphisms; Boolean algebras; katowice problem},
language = {eng},
number = {3},
pages = {271-291},
title = {Automorphisms of $(λ)/ℐ_\{κ\}$},
url = {http://eudml.org/doc/281807},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Paul Larson
AU - Paul McKenney
TI - Automorphisms of $(λ)/ℐ_{κ}$
JO - Fundamenta Mathematicae
PY - 2016
VL - 233
IS - 3
SP - 271
EP - 291
AB - We study conditions on automorphisms of Boolean algebras of the form $(λ)/ℐ_{κ}$ (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 automorphism of $(2^{κ})/ℐ_{κ⁺}$ which is trivial on all sets of cardinality κ⁺ is trivial, and that $MA_{ℵ₁}$ implies both that every automorphism of (ℝ)/Fin is trivial on a cocountable set and that every automorphism of (ℝ)/Ctble is trivial.
LA - eng
KW - automorphisms; Boolean algebras; katowice problem
UR - http://eudml.org/doc/281807
ER -