Small universal families of graphs on $\aleph_{\omega+1}$

James Cummings; Mirna Dzamonja; Charles Morgan

doi:10.1017/jsl.2015.65

Small universal families of graphs on $\aleph_{\omega+1}$

James Cummings, Mirna Dzamonja, Charles Morgan

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

22 Downloads (Pure)

Abstract

We prove that it is consistent that א_ω is strong limit, 2^{א_ω} is large and the universality number for graphs on א_{ω+1} is small. The proof uses Prikry forcing with interleaved collapsing.

Original language	English
Pages (from-to)	541-569
Number of pages	29
Journal	Journal of Symbolic Logic
Volume	81
Issue number	02
Early online date	29 Jun 2016
DOIs	https://doi.org/10.1017/jsl.2015.65
Publication status	Published - Jun 2016

Keywords

Universality
graphs
Prikry forcing
iterated forcing
master conditions
successors of singular cardinals
Laver indestructibility

Access to Document

10.1017/jsl.2015.65

arxivAccepted author manuscript, 537 KB

Nice Uncountable Constructions.
Dzamonja, M.
Leverhulme Trust
1/05/14 → 30/04/15
Project: Research
Combinational set theory at the successor of a singular cardinal: a marriage of a forcing axiom and a reflection principle
Dzamonja, M.
Engineering and Physical Sciences Research Council
1/10/10 → 15/03/14
Project: Research

Cite this

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title = "Small universal families of graphs on $\aleph_{\omega+1}$",

abstract = "We prove that it is consistent that א_ω is strong limit, 2^{א_ω} is large and the universality number for graphs on א_{ω+1} is small. The proof uses Prikry forcing with interleaved collapsing.",

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KW - Prikry forcing

KW - iterated forcing

KW - master conditions

KW - successors of singular cardinals

KW - Laver indestructibility

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Small universal families of graphs on $\aleph_{\omega+1}$

Abstract

Keywords

Access to Document

Projects

Nice Uncountable Constructions.

Combinational set theory at the successor of a singular cardinal: a marriage of a forcing axiom and a reflection principle

Cite this