Reverse Mathematics and parameter-free Transfer

2014/09/24 by Benno van den Berg, Berg, Benno van den, Sam Sanders +1 · 1 citation
Computer Science · Mathematics · #Computability, Logic, AI Algorithms #FOS: Mathematics #History and Theory of Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1409.6881

openalex publication_date 2014/09/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

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.

Cited by

• The strength of countable saturation

Related

• Some nonstandard equivalences in Reverse Mathematics
• A note on non-classical Nonstandard Arithmetic
• The effective content of Reverse Nonstandard Mathematics and the nonstandard content of effective Reverse Mathematics
• A functional interpretation for nonstandard arithmetic
• Nonstandard Analysis and Constructivism!