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Published in:
2003 | OriginalPaper | Chapter
Algebraic Properties of Rogers Semilattices of Arithmetical Numberings
Authors : Serikzhan Badaev, Sergey Goncharov, Sergey Podzorov, Andrea Sorbi
Published in: Computability and Models
Publisher: Springer US
Included in: Professional Book Archive
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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 n ≥ 2 is hereditarily undecidable; the class of all Rogers semilattices of a fixed level n ≥ 2 has an incomplete theory.