Π1-conservation of Combinatorial Principles Weaker than Ramsey’s Theorem for Pairs
نویسندگان
چکیده
We study combinatorial principles weaker than Ramsey’s theorem for pairs over the system RCA0 (Recursive Comprehension Axiom) with Σ2-bounding. It is shown that the principles of Cohesiveness (COH), Ascending and Descending Sequence (ADS), and Chain/Antichain (CAC) are all Π1-conservative over Σ2-bounding. In particular, none of these principles proves Σ 0 2induction.
منابع مشابه
Combinatorial principles weaker than Ramsey's Theorem for pairs
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