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

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
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DOI 10.1002/malq.201200025
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Reverse Mathematics and Order Theoretic Fixed Point Theorems.Takashi Sato & Takeshi Yamazaki - 2017 - Archive for Mathematical Logic 56 (3-4):385-396.

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