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Groundwork for weak analysis. (English) Zbl 1015.03056

The authors work with a second-order theory (BTFA), a fragment of arithmetic whose provably total functions are polynomial, introduced by the second author in “A feasible theory for analyis” [J. Symb. Log. 59, No. 3, 1001-1011 (1994; Zbl 0808.03043)]. Some elementary concepts of analysis are developed in this theory. It is shown that the elementary theory of the real closed ordered fields (RCOF) can be interpreted in BTFA. Since BTFA can be intepreted in Robinson’s arithmetic \(Q\), one gets as a corollary that RCOF is interpretable in \(Q\).

MSC:

03F35 Second- and higher-order arithmetic and fragments
03B30 Foundations of classical theories (including reverse mathematics)

Citations:

Zbl 0808.03043
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References:

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