On the strength of marriage theorems and uniformity |
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Authors: | Makoto Fujiwara Kojiro Higuchi Takayuki Kihara |
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Institution: | 1. Mathematical Institute, Tohoku University, , Aoba‐ku, Sendai, Miyagi, Japan;2. Department of Mathematics and Informatics, Faculty of Science, Chiba University, , Inage, Chiba, Japan;3. Japan Advanced Institute of Science and Technology, , Nomi, Ishikawa, Japan |
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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 or if computable expanding Hall condition or computable local finiteness for girls is weakened. In contrast, the provability of the marriage theorem is maintained in 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 , and investigate the sequential and Weihrauch strength of marriage theorems under that condition. |
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