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INTERVALS OF THE LATTICE OF COMPUTABLY ENUMERABLE SETS AND EFFECTIVE BOOLEAN ALGEBRAS

Published online by Cambridge University Press:  01 November 1997

ANDRÉ NIES
ANDRÉ NIES
Affiliation:
Department of Mathematics, The University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA
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Abstract

We prove that each interval of the lattice [Escr ] of c.e. sets under inclusion is either a boolean algebra or has an undecidable theory. This solves an open problem of Maass and Stob [11]. We develop a method to prove undecidability by interpreting ideal lattices, which can also be applied to degree structures from complexity theory. We also answer a question left open in [7] by giving an example of a non-definable subclass of [Escr ]* which has an arithmetical index set and is invariant under automorphisms.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 6 , November 1997 , pp. 683 - 692
Copyright
© The London Mathematical Society 1997

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