Journal of Symbolic Logic

Strengthening prompt simplicity

David Diamondstone and Keng Meng Ng

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We introduce a natural strengthening of prompt simplicity which we call strong promptness, and study its relationship with existing lowness classes. This notion provides a ≤wtt version of superlow cuppability. We show that every strongly prompt c.e. set is superlow cuppable. Unfortunately, strong promptness is not a Turing degree notion, and so cannot characterize the sets which are superlow cuppable. However, it is a wtt-degree notion, and we show that it characterizes the degrees which satisfy a wtt-degree notion very close to the definition of superlow cuppability.

Further, we study the strongly prompt c.e. sets in the context of other notions related promptness, superlowness, and cupping. In particular, we show that every benign cost function has a strongly prompt set which obeys it, providing an analogue to the known result that every cost function with the limit condition has a prompt set which obeys it. We also study the effect that lowness properties have on the behaviour of a set under the join operator. In particular we construct an array noncomputable c.e. set whose join with every low c.e. set is low.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 3 (2011), 946-972.

Dates
First available in Project Euclid: 6 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1309952528

Digital Object Identifier
doi:10.2178/jsl/1309952528

Mathematical Reviews number (MathSciNet)
MR2849253

Zentralblatt MATH identifier
1247.03074

Citation

Diamondstone, David; Ng, Keng Meng. Strengthening prompt simplicity. J. Symbolic Logic 76 (2011), no. 3, 946--972. doi:10.2178/jsl/1309952528. https://projecteuclid.org/euclid.jsl/1309952528


Export citation