One-element Rogers semilattices in the Ershov hierarchy

2021 ◽  
Vol 60 (4) ◽  
pp. 433-437
Author(s):  
S. A. Badaev ◽  
B. S. Kalmurzaev ◽  
N. K. Mukash ◽  
M. Mustafa
Keyword(s):  
Ershov Hierarchy

Weakly precomplete equivalence relations in the Ershov hierarchy

2019 ◽  
Vol 58 (3) ◽  
pp. 297-319
Author(s):  
N. A. Bazhenov ◽  
B. S. Kalmurzaev
Keyword(s):  
Equivalence Relations ◽  
Ershov Hierarchy

Turing jumps in the Ershov hierarchy

2011 ◽  
Vol 50 (3) ◽  
pp. 279-289
Author(s):  
M. Kh. Faizrakhmanov
Keyword(s):  
Ershov Hierarchy

CEA Operators and the Ershov Hierarchy

2021 ◽  
Vol 65 (8) ◽  
pp. 63-69
Author(s):  
M. M. Arslanov ◽  
I. I. Batyrshin ◽  
M. M. Yamaleev
Keyword(s):  
Ershov Hierarchy

scholarly journals Bounding computably enumerable degrees in the Ershov hierarchy

2006 ◽  
Vol 141 (1-2) ◽  
pp. 79-88 ◽  
Author(s):  
Angsheng Li ◽  
Guohua Wu ◽  
Yue Yang
Keyword(s):  
Ershov Hierarchy ◽  
Computably Enumerable

On Universal Pairs in the Ershov Hierarchy

2021 ◽  
Vol 62 (1) ◽  
pp. 23-31
Author(s):  
N. A. Bazhenov ◽  
M. Mustafa ◽  
S. S. Ospichev
Keyword(s):  
Ershov Hierarchy

scholarly journals Classifying equivalence relations in the Ershov hierarchy

2020 ◽  
Vol 59 (7-8) ◽  
pp. 835-864
Author(s):  
Nikolay Bazhenov ◽  
Manat Mustafa ◽  
Luca San Mauro ◽  
Andrea Sorbi ◽  
Mars Yamaleev
Keyword(s):  
Equivalence Relations ◽  
Special Focus ◽  
Ershov Hierarchy ◽  
Standard Tool ◽  
Algebraic Properties ◽  
Sigma 1 ◽  
Degree Structure ◽  
Computably Enumerable

Abstract Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $$\leqslant _c$$ ⩽ c . This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the $$\Delta ^0_2$$ Δ 2 0 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by $$\leqslant _c$$ ⩽ c on the $$\Sigma ^{-1}_{a}\smallsetminus \Pi ^{-1}_a$$ Σ a - 1 \ Π a - 1 equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.

scholarly journals Post's Programme for the Ershov Hierarchy

2007 ◽  
Vol 17 (6) ◽  
pp. 1025-1040 ◽  
Author(s):  
B. Afshari ◽  
G. Barmpalias ◽  
S. B. Cooper ◽  
F. Stephan
Keyword(s):  
Ershov Hierarchy
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