Mathematical Logic Quarterly 58 (6):417-423 (2012)

Abstract
We introduce the notion of τ-like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω-like means that every element has finitely many predecessors, while being ζ-like means that every interval is finite. We consider statements of the form “any τ-like partial order has a τ-like linear extension” and “any τ-like partial order is embeddable into τ” . Working in the framework of reverse mathematics, we show that these statements are equivalent either to equation image or to equation image over the usual base system equation image
Keywords reverse mathematics  linearizability  MSC (2010) Primary: 03B30  τ‐like  Linear extensions of partial order  Secondary: 06A07
Categories (categorize this paper)
DOI 10.1002/malq.201200025
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,447
Through your library

References found in this work BETA

Subsystems of Second-Order Arithmetic.Stephen G. Simpson - 2004 - Studia Logica 77 (1):129-129.

View all 8 references / Add more references

Citations of this work BETA

Reverse Mathematics and Order Theoretic Fixed Point Theorems.Takashi Sato & Takeshi Yamazaki - 2017 - Archive for Mathematical Logic 56 (3-4):385-396.

Add more citations

Similar books and articles

Interval Orders and Reverse Mathematics.Alberto Marcone - 2007 - Notre Dame Journal of Formal Logic 48 (3):425-448.
Questioning Constructive Reverse Mathematics.I. Loeb - 2012 - Constructivist Foundations 7 (2):131-140.
Open Questions in Reverse Mathematics.Antonio Montalbán - 2011 - Bulletin of Symbolic Logic 17 (3):431-454.
Reverse Mathematics: The Playground of Logic.Richard A. Shore - 2010 - Bulletin of Symbolic Logic 16 (3):378-402.
The Block Relation in Computable Linear Orders.Michael Moses - 2011 - Notre Dame Journal of Formal Logic 52 (3):289-305.
Nonexistence of Universal Orders in Many Cardinals.Menachem Kojman & Saharon Shelah - 1992 - Journal of Symbolic Logic 57 (3):875-891.
Decidable Discrete Linear Orders.M. Moses - 1988 - Journal of Symbolic Logic 53 (2):531-539.
Adding Linear Orders.Saharon Shelah & Pierre Simon - 2012 - Journal of Symbolic Logic 77 (2):717-725.

Analytics

Added to PP index
2013-10-31

Total views
11 ( #759,074 of 2,330,441 )

Recent downloads (6 months)
1 ( #584,494 of 2,330,441 )

How can I increase my downloads?

Downloads

My notes