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Safety, Absoluteness, and Computability

Authors Arnon Avron, Shahar Lev, Nissan Levi

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Author Details

Arnon Avron
  • School of Computer Science, Tel Aviv University, Tel Aviv, Israel
Shahar Lev
  • School of Computer Science, Tel Aviv University, Tel Aviv, Israel
Nissan Levi
  • School of Computer Science, Tel Aviv University, Tel Aviv, Israel

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Arnon Avron, Shahar Lev, and Nissan Levi. Safety, Absoluteness, and Computability. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.CSL.2018.8

Abstract

The semantic notion of dependent safety is a common generalization of the notion of absoluteness used in set theory and the notion of domain independence used in database theory for characterizing safe queries. This notion has been used in previous works to provide a unified theory of constructions and operations as they are used in different branches of mathematics and computer science, including set theory, computability theory, and database theory. In this paper we provide a complete syntactic characterization of general first-order dependent safety. We also show that this syntactic safety relation can be used for characterizing the set of strictly decidable relations on the natural numbers, as well as for characterizing rudimentary set theory and absoluteness of formulas within it.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • Dependent Safety
  • Computability
  • Absoluteness
  • Decidability
  • Domain Independence

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