## Abstract

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 L_{n}(A) , that consist of first order formulas with n free variables, and in affine spaces A^{n} 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 language | English |
---|---|

Article number | 49 |

Journal | Algebra Universalis |

Volume | 82 |

Issue number | 3 |

DOIs | |

State | Published - 1 Aug 2021 |

## Keywords

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

## ASJC Scopus subject areas

- Algebra and Number Theory
- Logic