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April 23, 20260 citationsOpen Access

Informational Set Theory

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ASAsa Smith

Key Points

  • The paper aims to establish a new mathematical framework called Informational Set Theory that emphasizes information conservation in set-theoretic identity.
  • Introduced the foundational concepts of Informational Set Theory (IST) and its axioms.
  • Defined the Law of Kept Data (A_KD) regarding information changes during transformations.
  • Proposed that, contrary to ZFC, transformations in IST maintain a net change of zero in information.
  • Demonstrated the implications of costless mappings in standard set theory versus information conservation in IST.

Abstract

This paper introduces Informational Set Theory (IST), a foundational mathematical framework that treats set-theoretic identity through the lens of informational conservation. While standard Zermelo-Fraenkel Set Theory (ZFC) treats mathematical operations as costless mappings, IST establishes the Law of Kept Data (AKD), an axiom requiring that the net change in information (Delta I) remains zero for any valid transformation.

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Cite This Study

Asa Smith (2026) studied this question.

synapsesocial.com/papers/69e9baa885696592c86ecacchttps://doi.org/10.5281/zenodo.19686311
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