Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 48, Number 3 (2007), 425-448.
Interval Orders and Reverse Mathematics
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.
Notre Dame J. Formal Logic Volume 48, Number 3 (2007), 425-448.
First available in Project Euclid: 13 August 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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.