Notre Dame Journal of Formal Logic 48 (3):425-448 (2007)

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
Keywords reverse mathematics   interval orders   proper interval orders
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DOI 10.1305/ndjfl/1187031412
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Foundational Aspects of Theories of Measurement.Dana Scott & Patrick Suppes - 1958 - Journal of Symbolic Logic 23 (2):113-128.

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