Geodesic
On bounded $m$-reducibilities
Algebra and discrete mathematics, no. 2 (2005), pp. 1-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

Conditions for classes ${\mathfrak F}^1,{\mathfrak F}^0$ of non-decreasing total one-place arithmetic functions to define reducibility $\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]\leftrightharpoons\{(A,B)|A,B\subseteq\mathbb N\ \\ (\exists r.f. \ h) (\exists f_1\in{\mathfrak F}^1)(\exists f_0\in{\mathfrak F}^0) $ $[A\le_m^h\,B\ \\ f_0\unlhd h\unlhd f_1]\}$ where $k\unlhd l$ means that function $l$ majors function $k$ almost everywhere are studied. It is proved that the system of these reducibilities is highly ramified, and examples are constructed which differ drastically $\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]$ from the standard $m$-reducibility with respect to systems of degrees. Indecomposable and recursive degrees are considered.
Keywords: bounded reducibilities, degrees of unsolvability, singular reducibility, cylinder, indecomposable degree. 
@article{ADM_2005_2_a0,
     author = {Vladimir N. Belyaev},
     title = {On bounded $m$-reducibilities},
     journal = {Algebra and discrete mathematics},
     pages = {1--19},
     publisher = {mathdoc},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_2_a0/}
}
TY  - JOUR
AU  - Vladimir N. Belyaev
TI  - On bounded $m$-reducibilities
JO  - Algebra and discrete mathematics
PY  - 2005
SP  - 1
EP  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2005_2_a0/
LA  - en
ID  - ADM_2005_2_a0
ER  - 
%0 Journal Article
%A Vladimir N. Belyaev
%T On bounded $m$-reducibilities
%J Algebra and discrete mathematics
%D 2005
%P 1-19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2005_2_a0/
%G en
%F ADM_2005_2_a0
Vladimir N. Belyaev. On bounded $m$-reducibilities. Algebra and discrete mathematics, no. 2 (2005), pp. 1-19. http://geodesic.mathdoc.fr/item/ADM_2005_2_a0/