## 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)

### Keywords:

weak analysis; polytime computability; interpretability

Zbl 0808.03043
Full Text:

### References:

 [1] Arithmetic, proof theory and computational complexity pp 247– (1993) [2] Subsystems of second-order arithmetic (1999) · Zbl 0909.03048 [3] DOI: 10.1002/malq.19960420102 · Zbl 0842.03041 [4] A feasible theory for analysis 59 pp 1001– (1994) · Zbl 0808.03043 [5] DOI: 10.1007/978-1-4612-3466-1_9 [6] Logic and computation pp 137– (1990) [7] DOI: 10.1002/malq.19960420123 · Zbl 0849.03045 [8] Logic and computation pp 51– (1990) [9] Computability and logic (1990) [10] Electronic Notes in Theoretical Computer Science 13 pp 34– (1998) [11] Proceedings of the logic colloquium (1996) 12 pp 115– (1998) [12] DOI: 10.1007/s001530050055 · Zbl 0882.03050 [13] Complexity theory of real functions (1991) [14] Mathematical logic (1967) · Zbl 0149.24309 [15] The art of computer programming, Seminumerical algorithms 2 (1981) [16] Models of Peano arithmetic 15 (1991) · Zbl 0744.03037 [17] Grundlagen der Mathematik two (1968) [18] DOI: 10.1007/BF01630810 · Zbl 0721.03042 [19] Metamathematics of first-order arithmetic (1993) · Zbl 0781.03047 [20] DOI: 10.1002/(SICI)1521-3870(200001)46:1<105::AID-MALQ105>3.0.CO;2-2 · Zbl 0942.03061 [21] Technical report (1958) [22] Arithmetic, proof theory and computational complexity pp 364– (1993) [23] DOI: 10.1016/0168-0072(86)90074-6 · Zbl 0603.03019 [24] DOI: 10.1016/S0049-237X(98)80054-2 [25] Predicative arithmetic (1986) · Zbl 0617.03002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.