| Abstract |
Recently, conservative extensions of Peano and Heyting arithmetic in the spirit of Nelson's axiomatic approach to Nonstandard Analysis, have been proposed. In this paper, we study the Transfer axiom of Nonstandard Analysis restricted to formulas without parameters. Based on this axiom, we formulate a base theory for the Reverse Mathematics
of Nonstandard Analysis and prove some natural reversals, and show that
most of these equivalences do not hold in the absence of parameter-free
Transfer.
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