On universal graphs without instances of CH

Saharon Shelah

doi:10.1016/0168-0072(84)90042-3

On universal graphs without instances of CH

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

24 Scopus citations

Abstract

We first prove the consistency of: there is a universal graph of power א₁<2^א₀ = 2^א₁=א₂. The consistency of the non-existence of a universal graph of power א₁ is trivial. Add א₂ Cohen generic reals. We then show that we can have 2^א₀=א₂<2^א₁, and get similar results for other cardinals.

Original language	English
Pages (from-to)	75-87
Number of pages	13
Journal	Annals of Pure and Applied Logic
Volume	26
Issue number	1
DOIs	https://doi.org/10.1016/0168-0072(84)90042-3
State	Published - Feb 1984

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title = "On universal graphs without instances of CH",

abstract = "We first prove the consistency of: there is a universal graph of power א1<2א0 = 2א1=א2. The consistency of the non-existence of a universal graph of power א1 is trivial. Add א2 Cohen generic reals. We then show that we can have 2א0=א2<2א1, and get similar results for other cardinals.",

author = "Saharon Shelah",

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AB - We first prove the consistency of: there is a universal graph of power א1<2א0 = 2א1=א2. The consistency of the non-existence of a universal graph of power א1 is trivial. Add א2 Cohen generic reals. We then show that we can have 2א0=א2<2א1, and get similar results for other cardinals.

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On universal graphs without instances of CH

Abstract

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