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].
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DOI 10.1142/s0219061314500019
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References found in this work BETA

Forcing in Proof Theory.Jeremy Avigad - 2004 - Bulletin of Symbolic Logic 10 (3):305-333.
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.

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