Заглавие | Subrecursive incomparability of the graphs of standard and dual Baire sequences |
Вид публикация | Journal Article |
Година на публикуване | 2022 |
Автори | Georgiev I |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 109 |
Start Page | 41 |
Pagination | 41-55 |
ISSN | 1313-9215 (Print) 2603-5529 (Online) |
ключови думи | Baire sequences, computable analysis, graphs of representations, irrational number representations, subrecursive classes |
Резюме | Our main question of interest is the existence or the non-existence of a subrecursive reduction between different representations of the irrational numbers. For any representation, considered as a total function, we consider the characteristic function of its graph. The graph is computably equivalent to the function itself, but not subrecursively equivalent. In some cases, the graph of a representation is subrecursively equivalent to an already known representation, but in other cases it is a new representation. In the present paper we undertake a systematic study of the graphs of standard and dual Baire sequences. By combining our new results with the previously known results on the graph of the continued fraction, we obtain a total of eight new subrecursive degrees, which lie strictly between the Dedekind cut and the continued fraction. |
DOI | 10.60063/GSU.FMI.109.41-55 |
Прикачен файл | Размер |
---|---|
109-041-055.pdf | 527.74 KB |