Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/102602
Title: ∑2 induction and infinite injury priority arguments, part III: Prompt sets, minimal pairs and shoenfield's conjecture
Authors: Chong, C.T. 
Qian, L.
Slaman, T.A.
Yang, Y. 
Issue Date: 2001
Source: Chong, C.T.,Qian, L.,Slaman, T.A.,Yang, Y. (2001). ∑2 induction and infinite injury priority arguments, part III: Prompt sets, minimal pairs and shoenfield's conjecture. Israel Journal of Mathematics 121 : 1-28. ScholarBank@NUS Repository.
Abstract: We prove that in every B∑2 model (one satisfies ∑2 collection axioms but not ∑2 induction), every recursively enumerable (r.e.) set is either prompt or recursive. Consequently, over the base theory ∑2 collection, the existence of r.e. minimal pairs is equivalent to ∑2 induction. We also refute Shoenfield's Conjecture in B∑2 models.
Source Title: Israel Journal of Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/102602
ISSN: 00212172
Appears in Collections:Staff Publications

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