Topologies of pointwise convergence in the first order languages and in affine spaces

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The Galois correspondence G between sets of logical formulas of the first order language L over a signature L and type definable sets over an L-structure A on the set A is extensively studied in the literature. The Stone topology is successfully applied in model theory. We investigate basic properties of the pointwise convergence topologies in languages Ln(A) , that consist of first order formulas with n free variables, and in affine spaces An over A, and compare these topologies with Stone topology and Zariski topology. In particular, we show, that Zariski topology is strongly weaker than the pointwise convergence topology and the pointwise convergence topology coincides with the Stone topology on a subset U of the first order language L(A) if and only if U is finite modulo logic equivalence of formulas.

Original languageEnglish
Article number49
JournalAlgebra Universalis
Issue number3
StatePublished - 1 Aug 2021


  • Affine space
  • First order language
  • Galois correspondence
  • Metrics
  • Pointwise convergence topology
  • Transformation semigroup
  • Zariski topology

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Logic


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