Published May 19, 2025 | Version v1
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The Nitescence Theorem: A Formal Resolution of the Incompleteness Paradox

Creators

  • 1. Independent Researcher

Description

Mathematics seems trapped by Gödel’s Incompleteness, yet progress endures. The Nitescence Theorem explains this paradox: by formalizing a relevance tuple—(consistency strength, expressive power, resolution power)—and introducing a tetravalent logic plus a canonical closure operator, any undecidable proposition in one framework becomes decidable in a more relevant one.


Key contributions:

  • Rigorous Formalization & Core Results: statement and proof in Z◦ type theory; well-foundedness of relevance ordering 
  • Relevance‐Driven Extensions: tetravalent logic framework and canonical closure operator that systematically resolves undecidability (Def. 3.1) 
  • Illustrative Case Studies: CH, CFSG, FLT, demonstrating the natural ascent along the relevance hierarchy
  • Philosophical Synthesis & Outlook: bridging pluralism and structural monism; prospects for automated theorem proving and quantum-logic extensions

Keywords:  Mathematical Logic • Tetravalent Logic • Canonical Closure Operator • Formal Systems • Undecidability • Consistency Strength • Relevance Ordering • Philosophy of Mathematics • Mathematical Structures • Type Theory • Metamathematics • Proof Theory • Formal Epistemology • Ordinal Analysis • Mathematical Progress • Structural Ascension • Structural Monism • Z◦ Type Theory • Theory Extensions.

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Dates

Created
2025-05-19
Preprint

References

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