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

Fundamenta Mathematicae (2016)

- Volume: 233, Issue: 3, page 271-291
- ISSN: 0016-2736

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topPaul Larson, and Paul McKenney. "Automorphisms of $(λ)/ℐ_{κ}$." Fundamenta Mathematicae 233.3 (2016): 271-291. <http://eudml.org/doc/281807>.

@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 -

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