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  1. On the strength of könig's duality theorem for countable bipartite graphs.Stephen G. Simpson - 1994 - Journal of Symbolic Logic 59 (1):113-123.
    Let CKDT be the assertion that for every countably infinite bipartite graph G, there exist a vertex covering C of G and a matching M in G such that C consists of exactly one vertex from each edge in M. (This is a theorem of Podewski and Steffens [12].) Let ATR0 be the subsystem of second-order arithmetic with arithmetical transfinite recursion and restricted induction. Let RCA0 be the subsystem of second-order arithmetic with recursive comprehension and restricted induction. We show that (...)
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  • Reverse mathematics and initial intervals.Emanuele Frittaion & Alberto Marcone - 2014 - Annals of Pure and Applied Logic 165 (3):858-879.
    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 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 countable partial order is scattered and does not contain infinite antichains if and only if it has countably many initial intervals. We (...)
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