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Logics and admissible rules of constructive set theories
Rosalie Iemhoff1, Robert Passmann2
1Department of Philosophy and Religious Studies, Utrecht University, Janskerkhof 13, 3512 BL Utrecht, The Netherlands.
Summary
This study explores the logical structure of constructive set theories, analyzing how extensibility impacts their logic. Researchers identified several extensible set theories, offering new directions for proof theory research.
Area of Science:
- Mathematical Logic
- Set Theory
- Proof Theory
Background:
- Constructive set theories are foundational systems in mathematics.
- Understanding their logical structure is crucial for foundational research.
- Extensibility is a key property influencing set theory behavior.
Purpose of the Study:
- To survey the logical structure of constructive set theories.
- To analyze the impact of extensibility on these theories.
- To identify and provide examples of extensible set theories.
Main Methods:
- Logical analysis of formal systems.
- Investigation of set-theoretic properties.
- Comparative study of different set theories.
Main Results:
- A comprehensive survey of the logical architecture of constructive set theories.
- Detailed analysis of the consequences of extensibility.
- Identification of specific extensible set theories.
Conclusions:
- Extensibility significantly shapes the logical structure of constructive set theories.
- The findings provide a basis for future research in proof theory and set theory.
- Several examples of extensible set theories are presented, contributing to the field.
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