Avoiding uniformity in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:math>enumeration degrees

Badillo, Liliana; Harris, Charles M.

doi:10.1016/j.apal.2014.04.008

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…The following particular case of the previous corollary can be seen as a generalization of a result in Badillo and Harris [2], stating that there is a nonzero low e-degree that caps with a nonzero low e-degree and a high e-degree:…”

Section: Bounding and Nonbounding Minimal Pairsmentioning

confidence: 82%

Initial Segments of the Enumeration Degrees

Ganchev¹,

Sorbi²

2016

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Using properties of${\cal K}$-pairs of sets, we show that every nonzero enumeration degreeabounds a nontrivial initial segment of enumeration degrees whose nonzero elements have all the same jump asa. Some consequences of this fact are derived, that hold in the local structure of the enumeration degrees, including: There is an initial segment of enumeration degrees, whose nonzero elements are all high; there is a nonsplitting high enumeration degree; every noncappable enumeration degree is high; every nonzero low enumeration degree can be capped by degrees of any possible local jump (i.e., any jump that can be realized by enumeration degrees of the local structure); every enumeration degree that bounds a nonzero element of strictly smaller jump, is bounding; every low enumeration degree below a non low enumeration degreeacan be capped belowa.

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Section: Bounding and Nonbounding Minimal Pairsmentioning

confidence: 82%

Initial Segments of the Enumeration Degrees

Ganchev¹,

Sorbi²

2016

J. symb. log.

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“…(In fact, for any

Σ_{2}^{0}

set

A \subseteq O

the class

scriptU

, comprising precisely those sets that are a ‐c.e. for some

a \in A

, is

‐uniform .) Hence, as a simple example, we can replace “

Π_{1}^{0}

‐rigid” by “ω‐c.e.‐rigid” in Theorem .…”

Section: Rigidity and η‐Like Computable Linear Orderingsmentioning

confidence: 99%

Automorphisms ofη-like computable linear orderings and Kierstead's conjecture

2016

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Abstract. We develop an approach to the longstanding conjecture of H.A. Kierstead concerning the character of strongly nontrivial automorphisms of computable linear orderings. Our main result is that for any η-like computable linear ordering B, such that B has no interval of order type η, and such that the order type of B is determined by a 0 ′ -limitwise monotonic maximal block function, there exists computable L ∼ = B such that L has no nontrivial Π 0 1 automorphism.

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Avoiding uniformity in theΔ20enumeration degrees

Cited by 2 publications

References 26 publications

Initial Segments of the Enumeration Degrees

Initial Segments of the Enumeration Degrees

Automorphisms ofη-like computable linear orderings and Kierstead's conjecture

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