The Fractal Foundations of Mathematics: Resolving Paradox and Incompleteness with the IFO

<p>We present a new foundation for mathematics based on the Ibaguner Fractal Operator (IFO). By replacing discrete sets with fractal sets (F-sets) and classical proof theory with a hyperbolic path integral formulation, we demonstrate the resolution of Bertrand Russell's Paradox and the evasion of the first incompleteness theorem...</p>

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-01-01
DOI
https://doi.org/10.13140/rg.2.2.24575.27040
Primary Topic
Diverse Scientific and Economic Studies
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

The Fractal Foundations of Mathematics: Resolving Paradox and Incompleteness with the IFO

Zenodo (CERN European Organization for Nuclear Research)
Diverse Scientific and Economic Studies
article

The Fractal Foundations of Mathematics: Resolving Paradox and Incompleteness with the IFO

article en

Abstract

<p>We present a new foundation for mathematics based on the Ibaguner Fractal Operator (IFO). By replacing discrete sets with fractal sets (F-sets) and classical proof theory with a hyperbolic path integral formulation, we demonstrate the resolution of Bertrand Russell's Paradox and the evasion of the first incompleteness theorem...</p>

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 36%
Diverse Scientific and Economic Studies
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

The Fractal Foundations of Mathematics: Resolving Paradox and Incompleteness with the IFO · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS