Negative universality results for graphs

S.-D. Friedman, and K. Thompson. "Negative universality results for graphs." Fundamenta Mathematicae 210.3 (2010): 269-283. <http://eudml.org/doc/282686>.

@article{S2010,
abstract = {It is shown that in many forcing models there is no universal graph at the successors of regular cardinals. The proof, which is similar to the well-known proof for Cohen forcing, is extended to show that it is consistent to have no universal graph at the successor of a singular cardinal, and in particular at $ℵ_\{ω+1\}$. Previously, little was known about universality at the successors of singulars. Analogous results show it is consistent not just that there is no single graph which embeds the rest, but that it takes the maximal number ($2^λ$ for graphs of size λ) to embed the rest.},
author = {S.-D. Friedman, K. Thompson},
journal = {Fundamenta Mathematicae},
keywords = {forcing models; universal graph; successors of regular cardinals},
language = {eng},
number = {3},
pages = {269-283},
title = {Negative universality results for graphs},
url = {http://eudml.org/doc/282686},
volume = {210},
year = {2010},
}

TY - JOUR
AU - S.-D. Friedman
AU - K. Thompson
TI - Negative universality results for graphs
JO - Fundamenta Mathematicae
PY - 2010
VL - 210
IS - 3
SP - 269
EP - 283
AB - It is shown that in many forcing models there is no universal graph at the successors of regular cardinals. The proof, which is similar to the well-known proof for Cohen forcing, is extended to show that it is consistent to have no universal graph at the successor of a singular cardinal, and in particular at $ℵ_{ω+1}$. Previously, little was known about universality at the successors of singulars. Analogous results show it is consistent not just that there is no single graph which embeds the rest, but that it takes the maximal number ($2^λ$ for graphs of size λ) to embed the rest.
LA - eng
KW - forcing models; universal graph; successors of regular cardinals
UR - http://eudml.org/doc/282686
ER -