2013/05/28 by Alexander Kreuzer, Alexander P. Kreuzer, Kreuzer, Alexander P.
Computer Science · Mathematics · #05D10 #54H20 #Advanced Algebra and Logic #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Primary: 03B30 #Secondary: 03F35 #math.LO #msc:03B30 #msc:03F35 #msc:05D10 #msc:54H20
paper · pdf · doi:10.48550/arxiv.1305.6530
openalex publication_date 2013/05/28 · arxiv created 2015/10/09 · arxiv updated 2015/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the existence of minimal idempotent ultrafilters (on N) in the style of reverse mathematics and higher-order reverse mathematics using the Auslander-Ellis theorem and variant thereof. We obtain that the existence of minimal idempotent ultrafilters restricted to countable algebras of sets is equivalent to the Auslander-Ellis theorem (AET) and that the existence of minimal idempotent ultrafilters as higher-order objects is Π12-conservative over a refinement of AET.