On the strength of marriage theorems and uniformity

Makoto Fujiwara, Kojiro Higuchi, Takayuki Kihara

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Kierstead showed that every computable marriage problem has a computable matching under the assumption of computable expanding Hall condition and computable local finiteness for boys and girls. The strength of the marriage theorem reaches WKL0 or ACA0 if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in RCA even if local finiteness for boys is completely removed. Using these conditions, we classify the strength of variants of marriage theorems in the context of reverse mathematics. Furthermore, we introduce another condition that also makes the marriage theorem provable in RCA0, and investigate the sequential and Weihrauch strength of marriage theorems under that condition.

Original languageEnglish
Pages (from-to)136-153
Number of pages18
JournalMathematical Logic Quarterly
Volume60
Issue number3
DOIs
Publication statusPublished - 2014
Externally publishedYes

ASJC Scopus subject areas

  • Logic

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