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- Title
ON IDEMPOTENT ULTRAFILTERS IN HIGHER-ORDER REVERSE MATHEMATICS.
- Authors
KREUZER, ALEXANDER P.
- Abstract
We analyze the strength of the existence of idempotent ultrafilters in higher-order reverse mathematics.Let $\left( {{{\cal U}_{{\rm{idem}}}}} \right)$ be the statement that an idempotent ultrafilter on ℕ exists. We show that over $ACA_0^\omega$, the higher-order extension of ACA0, the statement $\left( {{{\cal U}_{{\rm{idem}}}}} \right)$ implies the iterated Hindman’s theorem (IHT) and we show that $ACA_0^\omega + \left( {{{\cal U}_{{\rm{idem}}}}} \right)$ is ${\rm{\Pi }}_2^1$-conservative over $ACA_0^\omega + IHT$ and thus over $ACA_0^ +$.
- Subjects
IDEMPOTENTS; ULTRAFILTERS (Mathematics); REVERSE mathematics; MATHEMATICS theorems; STONE-Cech compactification
- Publication
Journal of Symbolic Logic, 2015, Vol 80, Issue 1, p179
- ISSN
0022-4812
- Publication type
Article
- DOI
10.1017/jsl.2014.58