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|Title:||∑2 induction and infinite injury priority arguments, part III: Prompt sets, minimal pairs and shoenfield's conjecture|
|Authors:||Chong, C.T. |
|Citation:||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|
|Appears in Collections:||Staff Publications|
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