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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms · Benford’s Law and Fraud Detection · Quantum Computing Algorithms and Architecture
