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Ultrafilters in reverse mathematics
Journal of Mathematical Logic 14 (1):1450001 (2014)
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 [Formula: see text].Other Versions
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Citations of this work
Conservativity of ultrafilters over subsystems of second order arithmetic.Antonio Montalbán & Richard A. Shore - 2018 - Journal of Symbolic Logic 83 (2):740-765.
On idempotent ultrafilters in higher-order reverse mathematics.Alexander P. Kreuzer - 2015 - Journal of Symbolic Logic 80 (1):179-193.
References found in this work
Ultrafilters and types on models of arithmetic.L. A. S. Kirby - 1984 - Annals of Pure and Applied Logic 27 (3):215-252.
An effective proof that open sets are Ramsey.Jeremy Avigad - 1998 - Archive for Mathematical Logic 37 (4):235-240.
Formalizing non-standard arguments in second-order arithmetic.Keita Yokoyama - 2010 - Journal of Symbolic Logic 75 (4):1199-1210.
Non-principal ultrafilters, program extraction and higher-order reverse mathematics.Alexander P. Kreuzer - 2012 - Journal of Mathematical Logic 12 (1):1250002-.
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