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Notions of compactness in weak subsystems of second order arithmetic

Published online by Cambridge University Press:  31 March 2017

Stephen G. Simpson
Affiliation:
Pennsylvania State University
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Publisher: Cambridge University Press
Print publication year: 2005

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References

[1] E., Bishop and D., Bridges, Constructive analysis, Springer-Verlag, Berlin, 1985.
[2] A., Blass, J., Hirst, and S. G., Simpson, Logical analysis of some theorems of combinatorics and topological dynamics,Logic and combinatorics (S. G., Simpson, editor), Contemporary Mathematics, vol. 65, American Mathematical Society, Providence, RI, 1986.
[3] D. K., Brown, Functional analysis in weak subsystems of second order arithmetic, Ph.D. thesis, The Pennsylvania State University, University Park, PA, 1987.
[4] D. K., Brown, Notions of closed subsets of a complete separable metric space in weak subsystems of second order arithmetic,Logic and computation(W., Sieg, editor), Contemporary Mathematics, vol. 106, AmericanMathematical Society, Providence, RI, 1990, pp. 39–50.
[5] D. K., Brown and S. G., Simpson, Which set existence axioms are necessary to prove the separable Hahn-Banach theorem?,Annals of Pure and Applied Logic, vol. 31 (1986), pp. 123–144.
[6] H., Friedman, Some systems of second order arithmetic with restricted induction (abstract),The Journal of Symbolic Logic, vol. 41 (1976), pp. 557–559.
[7] H., Friedman, S. G., Simpson, and R., Smith, Countable algebra and set existence axioms,Annals of Pure and Applied Logic, vol. 25 (1983), pp. 141–181.
[8] M., Giusto and A., Marcone, Lesbesgue numbers and Atsuji spaces in subsystems of secondorder arithmetic,Archive for Mathematical Logic, vol. 37 (1998), pp. 343–362.
[9] M., Giusto and S. G., Simpson, Located sets and reverse mathematics,The Journal of Symbolic Logic, to appear.
[10] S. G., Simpson, Which set existence axioms are needed to prove the Cauchy-Peano theorem for ordinary differential equations?,The Journal of Symbolic Logic, vol. 49 (1984), pp. 783–802.
[11] S. G., Simpson, Subsystems of second order arithmetic, Springer-Verlag, Berlin, 1999.
[12] H., Weyl, Das Kontinuum: Kritische Untersuchungen über die Grundlagen der Analysis, Berlin, 1917, reprinted by Chelsea, New York, NY, 1973.

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