On the order dimension of locally countable partial orderings-Reference-Cited by-同舟云学术

On the order dimension of locally countable partial orderings

Published:2020-02-26 Issue:7 Volume:148 Page:2823-2833
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Higuchi Kojiro,Lempp Steffen,Raghavan Dilip,Stephan Frank

Abstract

We show that the order dimension of any locally countable partial ordering ( P , > ) (P, >) of size κ + \kappa ^+ , for any κ \kappa of uncountable cofinality, is at most κ \kappa . In particular, this implies that it is consistent with ZFC that the dimension of the Turing degrees under partial ordering can be strictly less than the continuum.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2020-148-07/S0002-9939-2020-14946-5/proc14946_AM.pdf

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