Linear extensions of partial orders and Reverse Mathematics

Details Linear extensions of partial orders and Reverse Mathematics Linear extensions of partial orders and Reverse Mathematics

2012-03-23

arxiv.org/abs/1203.5207v2

Mathematics

Logic

8 pages, minor changes suggested by referee. To appear in MLQ - Mathematical Logic Quarterly

Scientific paper

We introduce the notion of \tau-like partial order, where \tau is one of the linear order types \omega, \omega*, \omega+\omega*, and \zeta. For example, being \omega-like means that every element has finitely many predecessors, while being \zeta-like means that every interval is finite. We consider statements of the form "any \tau-like partial order has a \tau-like linear extension" and "any \tau-like partial order is embeddable into \tau" (when \tau\ is \zeta\ this result appears to be new). Working in the framework of reverse mathematics, we show that these statements are equivalent either to B\Sigma^0_2 or to ACA_0 over the usual base system RCA_0.

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