Graduate studies at Western
Journal of Symbolic Logic 59 (1):113-123 (1994)
|Abstract||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 .) 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 CKDT is provable in ART0. Combining this with a result of Aharoni, Magidor, and Shore , we see that CKDT is logically equivalent to the axioms of ATR0, the equivalence being provable in RCA0|
|Keywords||Matchings coverings bipartite graph reverse mathematics second-order arithmetic subsystems|
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