Cupping with random sets
Duration: 55 mins 27 secs
About this item
| Description: |
Day, A (University of California, Berkeley)
Friday 06 July 2012, 14:00-15:00 |
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| Created: | 2012-07-11 11:23 |
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| Collection: | Semantics and Syntax: A Legacy of Alan Turing |
| Publisher: | Isaac Newton Institute |
| Copyright: | Day, A |
| Language: | eng (English) |
| Abstract: | A set X is ML-cuppable if there exists an incomplete Martin-Löf random R that joins X to zero jump. It is weakly ML-cuppable if there exists an incomplete Martin-Löf random R that joins X above zero jump. We prove that a set is K-trivial if and only if it is not weakly ML-cuppable. Further, we show that a set below zero jump is K-trivial if and only if it is not ML-cuppable. These results settle a question of Kučera, who introduced both cuppability notions. This is joint work with Joseph S. Miller. |
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