Preservation Theorems Through the Lens of Topology

Author Aliaume Lopez

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Aliaume Lopez
  • Université Paris-Saclay, ENS Paris-Saclay, CNRS, LSV, Gif-sur-Yvette, France


I thank Jean Goubault-Larrecq and Sylvain Schmitz for their help and support in writing this paper.

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Aliaume Lopez. Preservation Theorems Through the Lens of Topology. In 29th EACSL Annual Conference on Computer Science Logic (CSL 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 183, pp. 32:1-32:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of surjective morphisms, subclasses, sums, products, topological closures, and projective limits. Throughout the paper, we also integrate already known results into this new framework and show how it captures the essence of their proofs.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • Mathematics of computing → Discrete mathematics
  • Mathematics of computing → Point-set topology
  • Preservation theorem
  • Pre-spectral space
  • Noetherian space
  • Spectral space


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