We investigate initial segments and intervals of Rogers semilattices of arithmetical families. We prove that there exist intervals with different algebraic properties; the elementary theory of any Rogers semilattice at arithmetical level $nge 2$ is hereditarily undecidable; the class of all Rogers semilattices of a fixed level $nge 2$ has an incomplete theory.
Badaev, S., Goncharov, S., Podzorov, S., Sorbi, A. (2003). Algebraic properties of Rogers semilattices of arithmetical numberings. In S.B. Cooper, S. Goncharov (a cura di), Computability and Models. Perspectives East and West (pp. 45-77). Dordrecht : Kluwer.
Algebraic properties of Rogers semilattices of arithmetical numberings
SORBI, ANDREA
2003-01-01
Abstract
We investigate initial segments and intervals of Rogers semilattices of arithmetical families. We prove that there exist intervals with different algebraic properties; the elementary theory of any Rogers semilattice at arithmetical level $nge 2$ is hereditarily undecidable; the class of all Rogers semilattices of a fixed level $nge 2$ has an incomplete theory.
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https://hdl.handle.net/11365/423453