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In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of the initial intervals. The first theorem states that a partial order has no infinite antichains if and only if its initial intervals are finite unions of ideals. The second one asserts that a… (More)
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… (More)
We undertake the study of size-change analysis in the context of Reverse Mathematics. In particular, we prove that the SCT criterion [9, Theorem 4] is equivalent to IΣ 2 over RCA0.