Equivalenze tra teoremi: il programma di ricerca della reverse mathematics

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1. AHARONI, RON - MAGIDOR, MENACHEM - SHORE, RICHARD A., On the strength of König's duality theorem for infinite bipartite graphs, J. Combin. Theory Ser. B, 54, n. 2 (1992), 257-290. Zbl0754.05053MR1152453DOI10.1016/0095-8956(92)90057-5
2. AVIGAD, JEREMY, Number theory and elementary arithmetic, Philos. Math. (3), 11 (2003), 257-284. Zbl1050.03005MR2006194DOI10.1093/philmat/11.3.257
3. BROWN, DOUGLAS K., Notions of compactness in weak subsystems of second order arithmetic, In Simpson [23], 47-66. Zbl1087.03039MR2185427
4. CIESIELSKI, KRZYSZTOF, Set theory for the working mathematician, Cambridge University Press (1997), xii+236. Zbl0938.03067MR1475462DOI10.1017/CBO9781139173131
5. ERDŎS, P. - KOMJÁTH, P., Countable decompositions of ${ℝ}^2$ and ${ℝ}^3$, Discrete Comput. Geom., 5, n. 4 (1990), 325-331. MR1043714DOI10.1007/BF02187793
6. FRIEDMAN, HARVEY, Necessary uses of abstract set theory in finite mathematics, Adv. in Math., 60, n. 1 (1986), 92-122. Zbl0613.03028MR839484DOI10.1016/0001-8708(86)90004-6
7. FRIEDMAN, HARVEY, Finite functions and the necessary use of large cardinals, Ann. of Math. (2), 148, n. 3 (1998), 803-893. Zbl0941.03050MR1670057DOI10.2307/121032
8. FRIEDMAN, HARVEY - SIMPSON, STEPHEN G., Issues and problems in reverse mathematics, In Computability theory and its applications (Boulder, CO 1999), Amer. Math. Soc. (2000), 127-144. Zbl0967.03050MR1770738DOI10.1090/conm/257/04031
9. HILBERT, DAVID - BERNAYS, PAUL, Grundlagen der Mathematik. I, Springer-Verlag, Berlin (1968), xv+473. MR237246
10. HILBERT, DAVID - BERNAYS, PAUL, Grundlagen der Mathematik. II, Springer-Verlag, Berlin (1970), xiv+561. MR272596
11. HOWARD, PAUL - RUBIN, JEAN E., Consequences of the axiom of choice, American Mathematical Society, Providence RI (1998), viii+432. Zbl0947.03001MR1637107DOI10.1090/surv/059
12. HUMPHREYS, A. JAMES, Did Cantor need set theory?, In Simpson [23], 244-270. Zbl1097.03052MR2185439
13. KANAMORI, AKIHIRO, The higher infinite, Springer-Verlag, Berlin (1994), xxiv+536. Zbl0813.03034MR1321144
14. COLE KLEENE, STEPHEN, Introduction to metamathematics, D. Van Nostrand Co. Inc., NewYork, N.Y. (1952), x+550. MR51790
15. LÉVY, AZRIEL, Basic set theory, Springer-Verlag, Berlin (1979), xiv+391. MR533962
16. MILLMAN, RICHARD S. - PARKER, GEORGE D., Geometry, Springer-Verlag, New York (1991), xiv+370. MR1083550DOI10.1007/978-1-4612-4436-3
17. MUMMERT, CARL - SIMPSON, STEPHEN G., Reverse mathematics and ${\mathrm{\Pi }}_2^1$ comprehension, Bull. Symbolic Logic, 11, n. 4 (2005), 526-533. Zbl1106.03050MR2198712
18. RUBIN, HERMAN - RUBIN, JEAN E., Equivalents of the axiom of choice. II, Studies in Logic and the Foundations of Mathematics, North-Holland Publishing Co., 116 (1985), xxviii+322. Zbl0582.03033MR798475
19. SIMPSON, STEPHEN G., Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?J. Symbolic Logic, 49, n. 3 (1984), 783-802. Zbl0584.03039MR758929DOI10.2307/2274131
20. SIMPSON, STEPHEN G., Partial realizations of Hilbert's Program, J. Symbolic Logic, 53, n. 2 (1988), 349-363. Zbl0654.03003MR947843DOI10.2307/2274508
21. SIMPSON, STEPHEN G., On the strength of König's duality theorem for countable bipartite graphs, J. Symbolic Logic, 59, n. 1 (1994), 113-123. Zbl0798.03060MR1264968DOI10.2307/2275254
22. SIMPSON, STEPHEN G., Subsystems of second order arithmetic, Springer-Verlag, Berlin (1999), xiv+445. Zbl0909.03048MR1723993DOI10.1007/978-3-642-59971-2
23. STEPHEN G. SIMPSON editor, Reverse mathematics 2001. Lecture Notes in Logic. Association for Symbolic Logic, La Jolla, Ca, 2005. MR2186912
24. TAIT, WILLIAM W., Finitism, J. Philos., 78 (1981), 524-546. 
25. WEYL, HERMANN, Das Kontinuum: Kritische Untersuchungen über die Grundlagen der Analysis, Veit, Leipzig (1918).