English

Reduced Set Theory

Logic 2026-02-27 v4

Abstract

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.

Keywords

Cite

@article{arxiv.2311.18551,
  title  = {Reduced Set Theory},
  author = {Matthias Kunik},
  journal= {arXiv preprint arXiv:2311.18551},
  year   = {2026}
}

Comments

We have corrected some typos and improved our notation. 34 pages

R2 v1 2026-06-28T13:36:57.089Z