Nonstandard arithmetic and reverse mathematics

Bulletin of Symbolic Logic 12 (1):100-125 (2006)
Abstract
We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic
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    Sam Sanders (2010). Relative Arithmetic. Mathematical Logic Quarterly 56 (6):564-572.
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