Universal graphs and functions on ω1

Saharon Shelah; Juris Steprāns

doi:10.1016/j.apal.2021.102986

Universal graphs and functions on ω₁

Saharon Shelah, Juris Steprāns^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

It is shown to be consistent with various values of b, d and 2^ℵ₁ that there is a universal graph on ω₁. Moreover, it is also shown that it is consistent that there is a universal graph on ω₁ — in other words, a universal symmetric function from ω₁² to 2 — but no such function from ω₁² to ω. The method used relies on iterating well known reals, such as Miller and Laver reals, and alternating this with the PID forcing which adds no new reals. The last sections examine the question of set valued universal functions.

Original language	English
Article number	102986
Journal	Annals of Pure and Applied Logic
Volume	172
Issue number	8
DOIs	https://doi.org/10.1016/j.apal.2021.102986
State	Published - 1 Aug 2021

Bibliographical note

Publisher Copyright:
© 2021

Keywords

Cardinal invariants
Forcing
Universal graphs

Access to Document

10.1016/j.apal.2021.102986

Cite this

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