# CONSERVATIVITY OF ULTRAFILTERS OVER SUBSYSTEMS OF SECOND ORDER ARITHMETIC

@article{Montalbn2018CONSERVATIVITYOU,
title={CONSERVATIVITY OF ULTRAFILTERS OVER SUBSYSTEMS OF SECOND ORDER ARITHMETIC},
author={Antonio Montalb{\'a}n and Richard A. Shore},
journal={The Journal of Symbolic Logic},
year={2018},
volume={83},
pages={740 - 765}
}
• Published 1 June 2018
• Mathematics
• The Journal of Symbolic Logic
Abstract We extend the usual language of second order arithmetic to one in which we can discuss an ultrafilter over of the sets of a given model. The semantics are based on fixing a subclass of the sets in a structure for the basic language that corresponds to the intended ultrafilter. In this language we state axioms that express the notion that the subclass is an ultrafilter and additional ones that say it is idempotent or Ramsey. The axioms for idempotent ultrafilters prove, for example…
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