Logics and Admissible Rules of Constructive Set Theories
Rosalie Iemhoff, Robert Passmann
TL;DR
This paper surveys the logical structure of constructive set theories, explores the implications of extensibility on their logic, and provides examples of extensible theories to guide future research.
Contribution
It offers a comprehensive survey of constructive set theories' logic and introduces the concept of extensibility with concrete examples, highlighting new research directions.
Findings
Analysis of the logical consequences of extensibility
Identification of examples of extensible set theories
Directions for future research in constructive set theories
Abstract
We survey the logical structure of constructive set theories and point towards directions for future research. Moreover, we analyse the consequences of being extensible for the logical structure of a given constructive set theory. We finally provide examples of a number of set theories that are extensible.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Advanced Algebra and Logic · Semantic Web and Ontologies