Bibliography

1

Douglas K. Brown.
Functional Analysis in Weak Subsystems of Second Order Arithmetic.
PhD thesis, The Pennsylvania State University, 1987.
vii + 150 pages.

2

Douglas K. Brown.
Notions of closed subsets of a complete separable metric space in weak subsystems of second order arithmetic.
In [17], pages 39-50, 1990.

3

Douglas K. Brown and Stephen G. Simpson.
Which set existence axioms are needed to prove the separable Hahn-Banach theorem?
Annals of Pure and Applied Logic, 31:123-144, 1986.

4

Douglas K. Brown and Stephen G. Simpson.
The Baire category theorem in weak subsystems of second order arithmetic.
Journal of Symbolic Logic, 58:557-578, 1993.

5

Neil Cameron.
Introduction to Linear and Convex Programming.
Cambridge University Press, 1985.
149 pages.

6

John B. Conway.
A Course in Functional Analysis.
Springer-Verlag, 2nd edition, 1990.
XVI + 399 pages.

7

Harvey Friedman.
unpublished communication to Leo Harrington, 1977.

8

Mariagnese Giusto and Stephen G. Simpson.
Located sets and reverse mathematics.
Journal of Symbolic Logic, 1999.
37 pages, accepted August 1998, to appear.

9

Leo Harrington.
unpublished communication to Harvey Friedman, 1977.

10

Kostas Hatzikiriakou.
$\mathsf{WKL}_0$ and Stone's separation theorem for convex sets.
Annals of Pure and Applied Logic, 77:245-249, 1996.

11

A. James Humphreys.
On the Necessary Use of Strong Set Existence Axioms in Analysis and Functional Analysis.
PhD thesis, Pennsylvania State University, 1996.
viii + 83 pages.

12

A. James Humphreys and Stephen G. Simpson.
Separable Banach space theory needs strong set existence axioms.
Transactions of the American Mathematical Society, 348:4231-4255, 1996.

13

J. os and C. Ryll-Nardzewski.
On the application of Tychonoff's theorem in mathematical proofs.
Fundamenta Mathematicae, 38:233-237, 1951.

14

George Metakides, Anil Nerode, and Richard A. Shore.
On Bishop's Hahn-Banach theorem.
In [15], pages 85-91, 1985.

15

M. Rosenblatt, editor.
Errett Bishop, Reflections on Him and His Research, Contemporary Mathematics. American Mathematical Society, 1985.
xvii + 91 pages.

16

Naoki Shioji and Kazuyuki Tanaka.
Fixed point theory in weak second-order arithmetic.
Annals of Pure and Applied Logic, 47:167-188, 1990.

17

W. Sieg, editor.
Logic and Computation, Contemporary Mathematics. American Mathematical Society, 1990.
xiv + 297 pages.

18

Wilfried Sieg.
Fragments of arithmetic.
Annals of Pure and Applied Logic, 28:33-71, 1985.

19

Stephen G. Simpson.
Partial realizations of Hilbert's program.
Journal of Symbolic Logic, 53:349-363, 1988.

20

Stephen G. Simpson.
Subsystems of Second Order Arithmetic.
Perspectives in Mathematical Logic. Springer-Verlag, 1998.
XIV + 445 pages.