Geodesic
On the Embedding of~the~First Nonconstructive Ordinal
Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 764-774

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

The embedding of the first nonconstructive ordinal in the Rogers semilattices of families of arithmetic sets is considered. It is proved that, for any infinite family of arithmetic sets, the first nonconstructive ordinal can be embedded over any minimal element of its Rogers semilattice. It is also shown that if the family is principal or finite, then the first nonconstructive ordinal is embedded over any nongreatest element of its Rogers semilattice.
Keywords: numbering, Rogers semilattice, first nonconstructive ordinal. 
@article{MZM_2023_113_5_a11,
     author = {M. Kh. Faizrahmanov},
     title = {On the {Embedding} {of~the~First} {Nonconstructive} {Ordinal}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {764--774},
     publisher = {mathdoc},
     volume = {113},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a11/}
}
TY  - JOUR
AU  - M. Kh. Faizrahmanov
TI  - On the Embedding of~the~First Nonconstructive Ordinal
JO  - Matematičeskie zametki
PY  - 2023
SP  - 764
EP  - 774
VL  - 113
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a11/
LA  - ru
ID  - MZM_2023_113_5_a11
ER  - 
%0 Journal Article
%A M. Kh. Faizrahmanov
%T On the Embedding of~the~First Nonconstructive Ordinal
%J Matematičeskie zametki
%D 2023
%P 764-774
%V 113
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a11/
%G ru
%F MZM_2023_113_5_a11
M. Kh. Faizrahmanov. On the Embedding of~the~First Nonconstructive Ordinal. Matematičeskie zametki, Tome 113 (2023) no. 5, pp. 764-774. http://geodesic.mathdoc.fr/item/MZM_2023_113_5_a11/