Relativized Degree Spectra

2006 ◽  
pp. 546-555 ◽  
Author(s):  
Alexandra A. Soskova
Keyword(s):  
Degree Spectra

Degree Spectra of Structures

2021 ◽  
Author(s):  
I. Sh. Kalimullin ◽  
V. L. Selivanov ◽  
A. N. Frolov
Keyword(s):  
Degree Spectra

scholarly journals Π10 classes and strong degree spectra of relations

2007 ◽  
Vol 72 (3) ◽  
pp. 1003-1018 ◽  
Author(s):  
John Chisholm ◽  
Jennifer Chubb ◽  
Valentina S. Harizanov ◽  
Denis R. Hirschfeldt ◽  
Carl G. Jockusch ◽  
...  
Keyword(s):  
Kolmogorov Complexity ◽  
Initial Segment ◽  
Truth Table ◽  
Linear Ordering ◽  
Computable Structures ◽  
Degree Spectra

AbstractWe study the weak truth-table and truth-table degrees of the images of subsets of computable structures under isomorphisms between computable structures. In particular, we show that there is a low c.e. set that is not weak truth-table reducible to any initial segment of any scattered computable linear ordering. Countable subsets of 2ω and Kolmogorov complexity play a major role in the proof.

Relativized Degree Spectra

2007 ◽  
Vol 17 (6) ◽  
pp. 1215-1233 ◽  
Author(s):  
A. A. Soskova
Keyword(s):  
Degree Spectra

scholarly journals Degree Spectra of Structures Relative to Equivalences

2019 ◽  
Vol 58 (2) ◽  
pp. 158-172 ◽  
Author(s):  
P. M. Semukhin ◽  
D. Turetsky ◽  
E. B. Fokina
Keyword(s):  
Degree Spectra

New Degree Spectra of Polish Spaces

2021 ◽  
Vol 62 (5) ◽  
pp. 882-894
Author(s):  
A. G. Melnikov
Keyword(s):  
Polish Spaces ◽  
Degree Spectra

Degree spectra of intrinsically c.e. relations

2001 ◽  
Vol 66 (2) ◽  
pp. 441-469 ◽  
Author(s):  
Denis R. Hirschfeldt
Keyword(s):  
Computable Structure ◽  
Degree Spectra ◽  
Degree Spectrum

AbstractWe show that for every c.e. degree a > 0 there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is {0, a}. This result can be extended in two directions. First we show that for every uniformly c.e. collection of sets S there exists an intrinsically c.e. relation on the domain of a computable structure whose degree spectrum is the set of degrees of elements of S. Then we show that if α ∈ ω ∪ {ω} then for any α-c.e. degree a > 0 there exists an intrinsically α-c.e. relation on the domain of a computable structure whose degree spectrum {0, a}. All of these results also hold for m-degree spectra of relations.

Quasi-minimal degrees for degree spectra

2013 ◽  
Vol 23 (6) ◽  
pp. 1319-1334 ◽  
Author(s):  
A. A. Soskova ◽  
I. N. Soskov
Keyword(s):  
Degree Spectra

Degree spectra of relations on computable structures in the presence of Δ20 isomorphisms

2002 ◽  
Vol 67 (2) ◽  
pp. 697-720 ◽  
Author(s):  
Denis R. Hirschfeldt
Keyword(s):  
Point Of View ◽  
The Other ◽  
Computable Structure ◽  
Sufficient Condition ◽  
Computable Structures ◽  
Linear Orderings ◽  
Degree Spectra ◽  
Other Hand ◽  
Infinite Degree ◽  
Degree Spectrum

AbstractWe give some new examples of possible degree spectra of invariant relations on Δ20-categorical computable structures, which demonstrate that such spectra can be fairly complicated. On the other hand, we show that there are nontrivial restrictions on the sets of degrees that can be realized as degree spectra of such relations. In particular, we give a sufficient condition for a relation to have infinite degree spectrum that implies that every invariant computable relation on a Δ20-categorical computable structure is either intrinsically computable or has infinite degree spectrum. This condition also allows us to use the proof of a result of Moses [23] to establish the same result for computable relations on computable linear orderings.We also place our results in the context of the study of what types of degree-theoretic constructions can be carried out within the degree spectrum of a relation on a computable structure, given some restrictions on the relation or the structure. From this point of view we consider the cases of Δ20-categorical structures, linear orderings, and 1-decidable structures, in the last case using the proof of a result of Ash and Nerode [3] to extend results of Harizanov [14].

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