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{1187031412,
author = {Marcone, Alberto},
title = {Interval Orders and Reverse Mathematics},
journal = {Notre Dame J. Formal Logic},
volume = {48},
number = {1},
year = {2007},
pages = { 425-448},
language = {en},
url = {http://dml.mathdoc.fr/item/1187031412}
}
Marcone, Alberto. Interval Orders and Reverse Mathematics. Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, pp. 425-448. http://gdmltest.u-ga.fr/item/1187031412/