Notre Dame Journal of Formal Logic

Interval Orders and Reverse Mathematics

Alberto Marcone

Abstract

We study the reverse mathematics of interval orders. We establish the logical strength of the implications among various definitions of the notion of interval order. We also consider the strength of different versions of the characterization theorem for interval orders: a partial order is an interval order if and only if it does not contain 2 \oplus 2. We also study proper interval orders and their characterization theorem: a partial order is a proper interval order if and only if it contains neither 2 \oplus 2 nor 3 \oplus 1.

Article information

Source
Notre Dame J. Formal Logic Volume 48, Number 3 (2007), 425-448.

Dates
First available in Project Euclid: 13 August 2007

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1187031412

Digital Object Identifier
doi:10.1305/ndjfl/1187031412

Mathematical Reviews number (MathSciNet)
MR2336356

Zentralblatt MATH identifier
1135.03005

Subjects
Primary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]
Secondary: 06A06: Partial order, general 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]

Keywords
reverse mathematics interval orders proper interval orders

Citation

Marcone, Alberto. Interval Orders and Reverse Mathematics. Notre Dame J. Formal Logic 48 (2007), no. 3, 425--448. doi:10.1305/ndjfl/1187031412. http://projecteuclid.org/euclid.ndjfl/1187031412.


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