**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unpublished communication to Leo Harrington, 1977.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unpublished communication to Harvey Friedman, 1977.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.

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.