Ultrafilters in Reverse Mathematics
Henry Towsner
TL;DR
This paper explores the integration of non-principal ultrafilters into reverse mathematics, demonstrating that such extensions do not increase the strength of foundational theories like ACA0, ATR0, and Pi11-Comprehension.
Contribution
It introduces ultrafilters into reverse mathematics frameworks and proves these extensions are conservative over standard theories.
Findings
Ultrafilter extensions are conservative over ACA0, ATR0, and Pi11-Comprehension.
Ultrafilters can be incorporated without increasing the base theories' strength.
Theoretical framework for ultrafilters in reverse mathematics is established.
Abstract
We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA0, ATR0, and Pi11-Comprehension.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Benford’s Law and Fraud Detection · Quantum Computing Algorithms and Architecture