A Journey to Computably Enumerable Structures (Tutorial Lectures)

2018 ◽  
pp. 1-19
Author(s):  
Bakh Khoussainov
Keyword(s):  
Computably Enumerable

Ramsey's theorem for computably enumerable colorings

2001 ◽  
Vol 66 (2) ◽  
pp. 873-880 ◽  
Author(s):  
Tamara J. Hummel ◽  
Carl G. Jockusch
Keyword(s):  
Analogous Result ◽  
Computably Enumerable Set ◽  
Ramsey's Theorem ◽  
Ramsey’S Theorem ◽  
Computably Enumerable

AbstractIt is shown that for each computably enumerable set of n-element subsets of ω there is an infinite set A ⊆ ω such that either all n-element subsets of A are in or no n-element subsets of A are in . An analogous result is obtained with the requirement that A be replaced by the requirement that the jump of A be computable from 0(n). These results are best possible in various senses.

scholarly journals Definable properties of the computably enumerable sets

1998 ◽  
Vol 94 (1-3) ◽  
pp. 97-125 ◽  
Author(s):  
Leo Harrington ◽  
Robert I. Soare
Keyword(s):  
Computably Enumerable Sets ◽  
Computably Enumerable

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

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.

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