Effectiveness for the Dual Ramsey Theorem
نویسندگان
چکیده
We analyze the dual Ramsey theorem for k partitions and ℓ colors (DRTℓk) in context of reverse math, effective analysis, strong reductions. Over RCA0, stated Baire colorings Baire-DRTℓk is equivalent to statement clopen ODRTℓk a purely combinatorial CDRTℓk. When Borel k≥3, resulting principles are essentially relativizations For each α, there computable code Δα0-coloring such that any partition homogeneous it computes ∅(α) or ∅(α−1) depending on whether α infinite finite. k=2, we present partial results giving bounds content principle. A weaker version Δn0-reduced D2n over RCA0+IΣn−10 sense Weihrauch
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 2021
ISSN: ['0029-4527', '1939-0726']
DOI: https://doi.org/10.1215/00294527-2021-0024