In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and car-dinality 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… (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… (More)
We undertake the study of size-change analysis in the context of Reverse Mathematics. In particular, we prove that the SCT criterion is equivalent to $\Sigma^0_2$-induction over RCA$_0$.