We investigate differences in isomorphism types and elementary theories of Rogers semilattices of arithmetical numberings, depending on different levels of the arithmetical hierarchy. It is proved that new types of isomorphism appear as the arithmetical level increases. It is also proved the incompleteness of the theory of the class of all Rogers semilattices of any fixed level. Finally, no Rogers semilattice of any infinite family at arithmetical level $ngeq 2$ is weakly distributive, whereas Rogers semilattices of finite families are always distributive.

Badaev, S., Goncharov, S., Sorbi, A. (2003). Isomorphism types and theories of Rogers semilattices of arithmetical numberings. In S.B. Cooper, S. Goncharov (a cura di), Computability and Models. Perspectives East and West (pp. 79-91). Dordrecht : Kluwer [10.1007/978-1-4615-0755-0_4].

Isomorphism types and theories of Rogers semilattices of arithmetical numberings

SORBI, ANDREA
2003-01-01

Abstract

We investigate differences in isomorphism types and elementary theories of Rogers semilattices of arithmetical numberings, depending on different levels of the arithmetical hierarchy. It is proved that new types of isomorphism appear as the arithmetical level increases. It is also proved the incompleteness of the theory of the class of all Rogers semilattices of any fixed level. Finally, no Rogers semilattice of any infinite family at arithmetical level $ngeq 2$ is weakly distributive, whereas Rogers semilattices of finite families are always distributive.
2003
978-1-4613-5225-9
Badaev, S., Goncharov, S., Sorbi, A. (2003). Isomorphism types and theories of Rogers semilattices of arithmetical numberings. In S.B. Cooper, S. Goncharov (a cura di), Computability and Models. Perspectives East and West (pp. 79-91). Dordrecht : Kluwer [10.1007/978-1-4615-0755-0_4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/423454