Reduced Set Theory

We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation and with only finite or countably infinite ordinals. Still a...

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Bibliographic Details
Published in:arXiv.org 2024-10
Main Author: Kunik, Matthias
Format: Article
Language:English
Subjects:
Iterative methods
Set theory
Online Access:Get full text
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Summary:We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation and with only finite or countably infinite ordinals. Still a considerable part of mathematics can be formalized within this system.
ISSN:2331-8422