Omitting Types, Bounded Width and the Ability to Count

@article{Larose2009OmittingTB,
  title={Omitting Types, Bounded Width and the Ability to Count},
  author={Benoit Larose and Matthew Valeriote and L{\'a}szl{\'o} Z{\'a}dori},
  journal={IJAC},
  year={2009},
  volume={19},
  pages={647-668}
}
We say that a finite algebra A = 〈A; F 〉 has the ability to count if there are subalgebras C of A3 and Z of A such that the structure 〈A;C, Z〉 has the ability to count in the sense of Feder and Vardi. We show that for a core relational structure A the following conditions are equivalent: (i) the variety generated by the algebra A associated to A contains an algebra with the ability to count; (ii) A2 has the ability to count; (iii) the variety generated by A admits the unary or affine type. As a… CONTINUE READING

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