Consistency of the Silver dichotomy in generalised Baire space

@article{Sy2014,
abstract = {Silver’s fundamental dichotomy in the classical theory of Borel reducibility states that any Borel (or even co-analytic) equivalence relation with uncountably many classes has a perfect set of classes. The natural generalisation of this to the generalised Baire space $κ^\{κ\}$ for a regular uncountable κ fails in Gödel’s L, even for κ-Borel equivalence relations. We show here that Silver’s dichotomy for κ-Borel equivalence relations in $κ^\{κ\}$ for uncountable regular κ is however consistent (with GCH), assuming the existence of $0^\{#\}$.},
author = {Sy-David Friedman},
journal = {Fundamenta Mathematicae},
keywords = {Silver dichotomy; Silver indiscernibles; Borel reducibility; generalised Baire space},
language = {eng},
number = {2},
pages = {179-186},
title = {Consistency of the Silver dichotomy in generalised Baire space},
url = {http://eudml.org/doc/282958},
volume = {227},
year = {2014},
}

TY - JOUR
AU - Sy-David Friedman
TI - Consistency of the Silver dichotomy in generalised Baire space
JO - Fundamenta Mathematicae
PY - 2014
VL - 227
IS - 2
SP - 179
EP - 186
AB - Silver’s fundamental dichotomy in the classical theory of Borel reducibility states that any Borel (or even co-analytic) equivalence relation with uncountably many classes has a perfect set of classes. The natural generalisation of this to the generalised Baire space $κ^{κ}$ for a regular uncountable κ fails in Gödel’s L, even for κ-Borel equivalence relations. We show here that Silver’s dichotomy for κ-Borel equivalence relations in $κ^{κ}$ for uncountable regular κ is however consistent (with GCH), assuming the existence of $0^{#}$.
LA - eng
KW - Silver dichotomy; Silver indiscernibles; Borel reducibility; generalised Baire space
UR - http://eudml.org/doc/282958
ER -