Sbornik. Mathematics, Tome 199 (2008) no. 10, pp. 1451-1458
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I. Sh. Kalimullin. Almost computably enumerable families of sets. Sbornik. Mathematics, Tome 199 (2008) no. 10, pp. 1451-1458. http://geodesic.mathdoc.fr/item/SM_2008_199_10_a1/
@article{SM_2008_199_10_a1,
author = {I. Sh. Kalimullin},
title = {Almost computably enumerable families of sets},
journal = {Sbornik. Mathematics},
pages = {1451--1458},
year = {2008},
volume = {199},
number = {10},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2008_199_10_a1/}
}
TY - JOUR
AU - I. Sh. Kalimullin
TI - Almost computably enumerable families of sets
JO - Sbornik. Mathematics
PY - 2008
SP - 1451
EP - 1458
VL - 199
IS - 10
UR - http://geodesic.mathdoc.fr/item/SM_2008_199_10_a1/
LA - en
ID - SM_2008_199_10_a1
ER -
%0 Journal Article
%A I. Sh. Kalimullin
%T Almost computably enumerable families of sets
%J Sbornik. Mathematics
%D 2008
%P 1451-1458
%V 199
%N 10
%U http://geodesic.mathdoc.fr/item/SM_2008_199_10_a1/
%G en
%F SM_2008_199_10_a1
An almost computably enumerable family that is not $\varnothing'$-computably enumerable is constructed. Moreover, it is established that for any computably enumerable (c.e.) set $A$ there exists a family that is $X$-c.e. if and only if the set $X$ is not $A$-computable. Bibliography: 5 titles.
[1] H. Rogers, jr., Theory of recursive functions and effective computability, McGraw-Hill, New York–Toronto, ON–London, 1967 | MR | MR | Zbl | Zbl
[2] R. I. Soare, Recursively enumerable sets and degrees. A study of computable functions and computably generated sets, Perspect. Math. Logic, Springer-Verlag, Berlin, 1987 ; R. I. Soar, Vychislimo perechislimye mnozhestva i stepeni, Kazanskoe mat. obschestvo, Kazan, 2000 | MR | Zbl | MR | Zbl
[3] J. Stillwell, “Decidability of the “almost all” theory of degrees”, J. Symbolic Logic, 37:3 (1972), 501–506 | DOI | MR | Zbl
[4] S. Wehner, “Enumerations, countable structures and Turing degrees”, Proc. Amer. Math. Soc., 126:7 (1998), 2131–2139 | DOI | MR | Zbl
[5] S. Goncharov, V. Harizanov, J. Knight, Ch. McCoy, R. Miller, R. Solomon, “Enumerations in computable structure theory”, Ann. Pure Appl. Logic, 136:3 (2005), 219–246 | DOI | MR | Zbl