… Here a ce degree a is locally noncappable if there is a ce degree … locally noncappable.
Seetapun proved in his thesis [7] that every nonzero incomplete ce degree is locally noncappable…

… A recursively enumerable (re) degree a is locally noncappable if … We say that c witnesses
that a is locally noncappable. … deg(A ⊕ C) witnesses that a is locally noncappable. That is, C is …

… In Chapter 3, we study the locally noncappable degrees, and we prove that for any nonzero
… d > a witnessing that a is locally noncappable, and c ∨ d is high. This result implies that both …

… We prove that there exists a noncappable enumeration … depth of knowledge of specific local
structure (see for example … In particular, many basic questions concerning the local theory …

… all high; there is a nonsplitting high enumeration degree; every noncappable enumeration
degree is high; … local jump (ie, any jump that can be realized by enumeration degrees of the …

… As Ladner and Sasso [9] observed, however, distributivity can be locally carried over …
noncappable re wtt degrees. We show that all but one of the characterizations of the noncappable …

… and proposed the concept of locally noncappable as follows. … A ce degree a is called locally
noncappable if there is a ce degree c … Here c is a witness for the local noncappability of a. …

… We use M and NC to denote the set of all cappable and noncappable ce degrees, respectively.
… Before we discuss noncappable degrees, we mention the following result by Shore. We …

… noncappable degrees. Furthermore, NC coincides with five other apparently unrelated
subclasses of R: ENC, the effectively noncappable … , noncappable and effectively noncappable re …

… A great deal of what is known about the local structure is due to work done by Cooper himself,
or coauthored with other collaborators: the existence of noncappable e-degrees ([13]); the …