A Useful Undecidable Theory

Authors:
Victor L. Selivanov
Affiliations:
A.P. Ershov Institute of Informatics Systems, Siberian Division Russian Academy of Sciences, and Theoretische Informatik, Universität Würzburg,
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

Citing 3
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Abstract

We show that many so called discrete weak semilatticesconsidered earlier in a series of author's publications havehereditary undecidable first-order theories. Since such structuresappear naturally in some parts of computability theory, we obtainseveral new undecidability results. This applies e.g. to thestructures of complete numberings, of m-degrees of indexsets and of the Wadge degrees of partitions in the Baire space andω-algebraic domains.