A comparison of minimal systems for constructive analysis

Garyfallia Vafeiadou

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arXiv · 1808.00383

A comparison of minimal systems for constructive analysis

Garyfallia Vafeiadou

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Abstract

We establish a precise relation between M, a subsystem of the formal axiomatic system of intuitionistic analysis FIM of S. C. Kleene, and elementary analysis EL of A. S. Troelstra, two weak formal systems of two-sorted intuitionistic arithmetic, both widely used as basis for (various forms of) constructive analysis. We show that EL is weaker than M, by introducing an axiom schema CF_d asserting that every decidable predicate of natural numbers has a characteristic function. By similar arguments, we compare some more systems of two-sorted intuitionistic arithmetic, including the formal theory BIM of W. Veldman.

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Garyfallia Vafeiadou. 2018-08-01. A comparison of minimal systems for constructive analysis. https://arxiv.org/abs/1808.00383

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