What does this research mean for the field?

The Ibaguner Fractal Operator (IFO) is model-realizable in parametric fractal categories if ZFC is consistent and certain independent extension axioms are added. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to demonstrate the consistency of the Ibaguner Fractal Operator by incorporating new axioms into ZFC.

February 19, 2026Open Access

Axiomatic Consistency Schema for the Ibaguner Fractal Operator (IFO)

Key Points

The aim is to demonstrate the consistency of the Ibaguner Fractal Operator by incorporating new axioms into ZFC.
Introduced independent extension axioms (IFO1 to IFO3) over a typed index structure.
Explored the model realizability of the IFO operator in parametric fractal categories.
Confirmed the model realizability of the IFO operator system under specified conditions.
No resolution of the Continuum Hypothesis within ZFC was achieved.

Abstract

Consistency Status Theorem (Relative Consistency Statement). If ZFC is consistent and Axioms IFO1 through IFO3 are added as independent extension axioms over a typed index structure I, then the IFO operator system is model-realizable in parametric fractal categories. Remark. No statement here resolves the Continuum Hypothesis inside ZFC. Any such resolution would be conditional on the added IFO cardinal lift axiom.

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Cite This Study

SİNAN İBAGÜNER (Thu,) studied this question.

synapsesocial.com/papers/6996a768ecb39a600b3ecfc4 https://doi.org/https://doi.org/10.13140/rg.2.2.34634.02248

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