Chapter 21 Reverse algebra

Studies in Logic and the Foundations of Mathematics

Volumn 139, Issue C, 1998, Pages 1355-1372

  Simpson, S G ^a   Rao, J ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

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EID: 77956739624     PISSN: 0049237X     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0049-237X(98)80054-2     Document Type: Article

References (25)

1. addendum. Friedman H.M., Simpson S.G., and Smith R.L. Countable algebra and set existence axioms. Ann. Pure Appl. Logic 25 (1983) 141-181
2. Friedman H.M., Simpson S.G., and Smith R.L. Countable algebra and set existence axioms. Ann. Pure Appl. Logic 27 (1985) 319-320
3. Hatzikiriakou K. Commutative algebra in subsystems of second order arithmetic. Ph.D. Thesis, Penn. State Univ., University Park, PA (1989)
4. 0 induction. Arch. Math. Logic 29 (1989) 47-51
5. Hatzikiriakou K. Minimal prime ideals and arithmetic comprehension. J. Symbolic Logic 56 (1991) 67-70
6. 0 and Stone's separation theorem for convex sets. Ann. Pure Appl. Logic 77 (1996) 245-249
7. Hatzikiriakou K., and Simpson S.G. Countable valued fields in weak subsystems of second-order arithmetic. Ann. Pure Appl. Logic 41 (1989) 27-32
8. 0 and orderings of countable abelian groups. In: Sieg W. (Ed). Logic and Computation, (Proc. Workshop, cmu, Pittsburg, June 30-July 2, 1987). Contemp. Math. 106 (1990) 177-180
9. J. Rao, Some topics in reverse algebra, Ph.D. Thesis, Penn. State Univ., University Park, PA, (in preparation).
10. J. Rao and S. G. Simpson, Factorization in subsystems of second order arithmetic, (in preparation).
11. Simpson S.G. Ordinal numbers and the Hilbert basis theorem. J. Symbolic Logic 53 (1988) 961-974
12. S. G. Simpson, Subsystems of Second Order Arithmetic, (in preparation).
13. 0 Induction. Ann. Pure Appl. Logic 31 (1986) 289-306
14. (translated from Russian and edited by G. Asser and H.-D. Hecker). Ershov Yu.L. Theorie der Numerierungen, III. Z. Math. Logik Grundlag. Math. 23 (1977) 289-371
15. Friedman H.M. Higher set theory and mathematical practice. Ann. Math. Logic 2 (1971) 325-357
16. Fröhlich A., and Shepherdson J.C. Effective procedures in field theory. Philos. Trans. Roy. Soc. London, Ser. A 248 (1956) 407-432
17. 1939; [2nd. edn. (1968, 1970)]. Hilbert D., and Bernays P. Grundlagen der Mathematik Vol. I, II (1934), Springer, Reading, Mass.
18. 0 classes and degrees of theories. Trans. Amer. Math. Soc. 173 (1972) 33-56
19. Oxford Logic Guides, 15. Kaye R. Models of Peano Arithmetic (1991), Oxford Univ. Press, Berlin
20. Metakides G., and Nerode A. Effective content of field theory. Ann. Math. Logic 17 (1979) 289-320
21. Rabin M.O. Computable algebra, general theory and theory of computable fields. Trans. Amer. Math. Soc. 95 (1960) 341-360
22. Shoenfield J.R. Mathematical Logic (1967), Addison-Wesley, NY
23. Simpson S.G. Degrees of unsolvability: a survey of results. In: Barwise J. (Ed). Handbook of Mathematical Logic, Stud. Logic Found. Math., 90 (1977) 631-652
24. Simpson S.G. Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?. J. Symbolic Logic 49 (1984) 783-802
25. 2 and reverse mathematics, appendix to Proof Theory. 2nd edn. In: Takeuti G. (Ed) (1987), North Holland 432-446