A Useful Undecidable Theory

Abstract. We show that many so called discrete weak semilattices considered earlier in a series of author’s publications have hereditary undecidable first-order theories. Since such structures appear naturally in some parts of computability theory, we obtain several new undecidability results. This applies e.g. to the structures of complete numberings, of m-degrees of index sets and of the Wadge degrees of partitions in the Baire space and ω-algebraic domains. Keywords. Semilattice, discrete weak semilattice, partition, reducibility, undecidability, theory.

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: Victor L. Selivanov
• Keywords: CIE 2007, Computability Theory, Discrete Weak Semilattice, Undecidable first-order Theories