Заглавие | ON THE NOTION OF JUMP STRUCTURE |
Вид публикация | Journal Article |
Година на публикуване | 2015 |
Автори | Vatev S |
Списание | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Том | 102 |
Pagination | 171-206 |
ISSN | 0205-0808 |
ключови думи | computability, definability, structures |
Резюме | For a given countable structure $\mathfrak{A}$ and a computable ordinal $\alpha$, we define its $\alpha$-th jump structure $\mathfrak{A}^{(\alpha)}$. We study how the jump structure relates to the original structure. We consider a relation between structures called conservative extension and show that $\mathfrak{A}^{(\alpha)}$ conservatively extends the structure $\mathfrak{A}$. It follows that the relations definable in $\mathfrak{A}$ by computable infinitary $\sum_{\alpha}$ formulae are exactly the relations definable in $\mathfrak{A}^{(\alpha)}$ by computable infinitary $\sum_{1}$ formulae. Moreover, the Turing degree spectrum of $\mathfrak{A}^{(\alpha)}$ is equal to the $\alpha$′-th jump Turing degree spectrum of $\mathfrak{A}$, where $\alpha′ = \alpha + 1,\text{ if } \alpha < \omega\text{, and }\alpha′ = \alpha$, otherwise. |
2000 MSC | 03D45, 03D30 |
Прикачен файл | Размер |
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102-171-206.pdf | 363.1 KB |