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Non-principal ultrafilters, program extraction and higher-order reverse mathematics

Alexander P. Kreuzer

Journal of Mathematical Logic 12 (1):1250002- (2012)

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Ultrafilters in reverse mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.details 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]. Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 2 citations
Transfinite recursion in higher reverse mathematics.Noah Schweber - 2015 - Journal of Symbolic Logic 80 (3):940-969.details Logic and Philosophy of Logic Logic and Philosophy of Logic, Miscellaneous in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 6 citations
Conservativity of ultrafilters over subsystems of second order arithmetic.Antonio Montalbán & Richard A. Shore - 2018 - Journal of Symbolic Logic 83 (2):740-765.details Logic and Philosophy of Logic Direct download (2 more) Export citation Bookmark 1 citation
On idempotent ultrafilters in higher-order reverse mathematics.Alexander P. Kreuzer - 2015 - Journal of Symbolic Logic 80 (1):179-193.details Logic and Philosophy of Logic Model Theory in Logic and Philosophy of Logic Direct download (3 more) Export citation Bookmark 1 citation

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