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arXiv · 2009.03185

Short Axiomatization of Stratified Comprehension

Zuhair A. Al-Johar
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Abstract

Several finite axiomatizations of stratified comprehension are known. This paper gives five set existence principles which, in the presence of Extensionality, yield the fourteen set-construction principles used in the finite basis recorded by Holmes. In addition, a direct unordered proof is given showing that the same five principles, together with extensionality only for nonempty sets, already imply every stratified comprehension instance, without passing through the Holmes ordered-pair machinery. The displayed reductions for unordered products, Cartesian products, and ordered relative products have been corrected. The original Holmes-basis reduction and the new direct weak-extensionality development have been checked by the Lean 4 kernel; the complete Lean source is supplied with this version.

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Zuhair A. Al-Johar. 2026-09-22. Short Axiomatization of Stratified Comprehension. https://arxiv.org/abs/2009.03185

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