Minimal Predicates for Δ-Definability

We consider two kinds of reducibilities on finite families of predicates on a countable set: the definability of predicates and their complements of one family via another by means of existential formulas with parameters and the same definability on isomorphism types of families. Ordered structures of degrees generated by families of unary predicates are described. It is proved that for both reducibilities, there exist continuum many minimal nonzero degrees.

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Correspondence to A. S. Morozov.

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D. A. Tussupov is Supported by KN MON RK (project No. AP08855497).

A. S. Morozov is Supported by SB RAS Fundamental Research Program I.1.1 (project No. 0314-2019-0003).

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Morozov, A.S., Tussupov, D.A. Minimal Predicates for Δ-Definability. Algebra Logic 59, 328–340 (2020). https://doi.org/10.1007/s10469-020-09605-9

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Keywords

  • Δ-definability
  • existential formula
  • ordered structure of degrees
  • minimal degrees