Geodesic
Distributive lattices of numberings
Algebra i logika, Tome 46 (2007) no. 1, pp. 83-102.

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

We study into a semilattice of numberings generated by a given fixed numbering via operations of completion and taking least upper bounds. It is proved that, except for the trivial cases, this semilattice is an infinite distributive lattice every principal ideal in which is finite. The least upper and the greatest lower bounds in the semilattice are invariant under extensions in the semilattice of all numberings. Isomorphism types for the semilattices in question are in one-to-one correspondence with pairs of cardinals the first component of which is equal to the cardinality of a set of non-special elements, and the second – to the cardinality of a set of special elements, of the initial numbering.
Keywords: numbering, complete numbering, completion, special element, upper semilattice of numberings. 
@article{AL_2007_46_1_a5,
     author = {Z. G. Khisamiev},
     title = {Distributive lattices of numberings},
     journal = {Algebra i logika},
     pages = {83--102},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_1_a5/}
}
TY  - JOUR
AU  - Z. G. Khisamiev
TI  - Distributive lattices of numberings
JO  - Algebra i logika
PY  - 2007
SP  - 83
EP  - 102
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2007_46_1_a5/
LA  - ru
ID  - AL_2007_46_1_a5
ER  - 
%0 Journal Article
%A Z. G. Khisamiev
%T Distributive lattices of numberings
%J Algebra i logika
%D 2007
%P 83-102
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2007_46_1_a5/
%G ru
%F AL_2007_46_1_a5
Z. G. Khisamiev. Distributive lattices of numberings. Algebra i logika, Tome 46 (2007) no. 1, pp. 83-102. http://geodesic.mathdoc.fr/item/AL_2007_46_1_a5/

[1] V. L. Selivanov, “O strukture stepenei obobschennykh indeksnykh mnozhestv”, Algebra i logika, 21:4 (1982), 472–491 | MR

[2] V. L. Selivanov, “Bulevy ierarkhii razbienii nad redutsiruemoi bazoi”, Algebra i logika, 43:1 (2004), 77–109 | MR | Zbl

[3] D. Spreen, “Strong reducibility of partial numberings”, Arch. Math. Logic, 44:2 (2005), 209–217 | DOI | MR | Zbl

[4] S. A. Badaev, S. S. Goncharov, A. Sorbi, “Completeness and universality of arithmetical numberings”, Computability and models, eds. S. B. Cooper, S. S. Goncharov, Kluwer Academic/Plenum Publishers, New York, 2003, 11–44 | MR

[5] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977 | MR

[6] Z. G. Khisamiev, “O podsemeistvakh osobykh elementov polnykh numeratsii”, Algebra i logika, 45:6 (2006), 758–764 | MR | Zbl