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De Zolt’s postulate is a more mathematically precise restatement of Euclid’s geometric principle of “the whole is greater than the part” [8, Book I, Common Notion 5]. While the three-dimensional version of De Zolt’s postulate is not consistent with ZFC due to the Banach-Tarski paradox and related theorems, it is consistent with a proof-theoretically weaker theory. In this paper, we provide an implementation of such a weak type theory and a formal proof of De Zolt’s postulate in three dimensions in this theory.

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A Proof of the De Zolt Postulate in Three-Dimensional Space

  • 会议论文

  • 发表日期：

    2026年

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  • Bruno Cuconato,
  • Edward Hermann Haeusler

摘要

De Zolt’s postulate is a more mathematically precise restatement of Euclid’s geometric principle of “the whole is greater than the part” [8, Book I, Common Notion 5]. While the three-dimensional version of De Zolt’s postulate is not consistent with ZFC due to the Banach-Tarski paradox and related theorems, it is consistent with a proof-theoretically weaker theory. In this paper, we provide an implementation of such a weak type theory and a formal proof of De Zolt’s postulate in three dimensions in this theory.