Journal of Symbolic Logic

Limits on jump inversion for strong reducibilities

Barbara F. Csima, Rod Downey, and Keng Meng Ng

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We show that Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a Δ02 set B >tt ∅' such that there is no c.e. set A with A' ≡wtt B. We also show that there is a Σ02 set C >tt ∅' such that there is no Δ02 set D with D' ≡wtt C.

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J. Symbolic Logic Volume 76, Issue 4 (2011), 1287-1296.

First available in Project Euclid: 11 October 2011

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Csima, Barbara F.; Downey, Rod; Ng, Keng Meng. Limits on jump inversion for strong reducibilities. J. Symbolic Logic 76 (2011), no. 4, 1287--1296. doi:10.2178/jsl/1318338849.

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