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2

R. Aharoni, M. Magidor, and R. A. Shore, On the strength of König's duality theorem for infinite bipartite graphs, Journal of Combinatorial Theory (B), 54, 1992, pp. 257-290.

3

A. R. Blass, J. L. Hirst, and S. G. Simpson, Logical analysis of some theorems of combinatorics and topological dynamics, in [8], pp. 125-156.

4

H. Friedman, Subsystems of set theory and analysis, Ph. D. Thesis, M. I. T., 1967, 83 pp.

5

H. Friedman, Systems of second order arithmetic with restricted induction I, II (abstracts), Journal of Symbolic Logic, 41, 1976, pp. 557-559.

6

H. M. Friedman, K. McAloon, and S. G. Simpson, A finite combinatorial principle which is equivalent to the 1-consistency of predicative analysis, in [11], pp. 197-230.

7

D. König, Theorie der Endlichen und Unendlichen Graphen, Akademische Verlagsgesellschaft, Leipzig, 1936, reprinted by Chelsea, New York, 1950, 258 pp.

8

Logic and Combinatorics, edited by S. G. Simpson, Contemporary Mathematics, American Mathematical Society, Providence, 1987, 384 pp.

9

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10

A. Marcone, Borel quasi-orderings in subsystems of second-order arithmetic, Annals of Pure and Applied Logic, 54, 1991, pp. 265-291.

11

Patras Logic Symposion, edited by G. Metakides, North-Holland, Amsterdam, 1982, 391 pp.

12

K. P. Podewski and K. Steffens, Injective choice functions for countable families, Journal of Combinatorial Theory (B), 21, 1976, pp. 40-46.

13

H. Rogers, Jr., Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York, 1967, reprinted by M.I.T. Press, Cambridge, 1987, 482 pp.

14

S. G. Simpson, Set-theoretic aspects of $\mathsf{ATR}_0$, in [9], pp. 255-271.

15

S. G. Simpson, $\Sigma^1_1$ and $\Pi^1_1$ transfinite induction, in [9], pp. 239-253.

16

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17

S. G. Simpson, Subsystems of Second Order Arithmetic, in preparation.

18

G. Takeuti, Proof Theory (Second Edition), North-Holland, Amsterdam, 1987, 490 pp.