Bulletin of the American Mathematical Society

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Book Information:

Author: Yiannis N. Moschovakis
Title: Descriptive set theory
Additional book information: Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Company, Amsterdam, 1980, xii + 637 pp.,$73.25.

1.

P. Aleksandrov, Sur la puissance des ensembles measurables B, C. R. Acad. Sci. U. S. A. 162 (1916), 323-325.

2.

R. Baire, Sur les fonctions de variables réelles, Annali di Mat. Ser. III 3 (1899), 1-123.

Ivar Bendixson, Quelques theorèmes, Acta Math. 2 (1883), no. 1, 415–429 (French). De la théorie des ensembles de points Extrait d’une lettre adressée à M. Cantor à Halle. MR 1554609, DOI 10.1007/BF02415227

David Blackwell, Infinite games and analytic sets, Proc. Nat. Acad. Sci. U.S.A. 58 (1967), 1836–1837. MR 221466, DOI 10.1073/pnas.58.5.1836

5.

E. Borel, Leçons sur la théorie des fonctions, Gauthier-Villars, Paris, 1898.

6.

E. Borel, Leçons sur les fonctions de variables réelles, Gauthier-Villars, Paris, 1905.

Paul Cohen, The independence of the continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 1143–1148. MR 157890, DOI 10.1073/pnas.50.6.1143

8.

S. Feferman and A. Lévy, Independence results in set theory by Cohen's method. II, Notices Amer. Math. Soc. 10 (1963), 593.

David Gale and F. M. Stewart, Infinite games with perfect information, Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, Princeton University Press, Princeton, N.J., 1953, pp. 245–266. MR 0054922

Kurt Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I, Monatsh. Math. Phys. 38 (1931), no. 1, 173–198 (German). MR 1549910, DOI 10.1007/BF01700692

11.

K. Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis, Proc. Nat. Acad. Sci. U. S. A. 24 (1938), 556-557.

Leo Harrington, Analytic determinacy and $0^{\sharp }$, J. Symbolic Logic 43 (1978), no. 4, 685–693. MR 518675, DOI 10.2307/2273508

F. Hausdorff, Die Mächtigkeit der Borelschen Mengen, Math. Ann. 77 (1916), no. 3, 430–437 (German). MR 1511869, DOI 10.1007/BF01475871

Stephen Cole Kleene, Introduction to metamathematics, D. Van Nostrand Co., Inc., New York, N. Y., 1952. MR 0051790

15.

M. Kondô, Sur l'uniformisation des complémentaires analytiques et les ensembles projectifs de la seconde class, Japan J. Math. 15 (1938), 197-230.

16.

H. Lebesgue, Intégrale, longuer, aire, Thèse, Paris, 1902.

17.

H. Lebesgue, Sur les fonctions représentables analytiquement, Journal de Math. Sér. 6 1 (1905), 139-216.

Donald A. Martin, Measurable cardinals and analytic games, Fund. Math. 66 (1969/70), 287–291. MR 258637, DOI 10.4064/fm-66-3-287-291

Donald A. Martin, Borel determinacy, Ann. of Math. (2) 102 (1975), no. 2, 363–371. MR 403976, DOI 10.2307/1971035

Donald A. Martin, Infinite games, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 269–273. MR 562614

Donald A. Martin, A theorem on hyperhypersimple sets, J. Symbolic Logic 28 (1963), 273–278. MR 177887, DOI 10.2307/2271305

Jan Mycielski and H. Steinhaus, A mathematical axiom contradicting the axiom of choice, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 1–3. MR 140430

Jan Mycielski and S. Świerczkowski, On the Lebesgue measurability and the axiom of determinateness, Fund. Math. 54 (1964), 67–71. MR 161788, DOI 10.4064/fm-54-1-67-71

W. Sierpiński, Les ensembles projectifs et analytiques, Mémor. Sci. Math., no. 112, Gauthier-Villars, Paris, 1950 (French). MR 0052484

Jack H. Silver, Counting the number of equivalence classes of Borel and coanalytic equivalence relations, Ann. Math. Logic 18 (1980), no. 1, 1–28. MR 568914, DOI 10.1016/0003-4843(80)90002-9

Robert M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1–56. MR 265151, DOI 10.2307/1970696

27.

M. Suslin, Sur une définition des ensembles measurables B sans nombres transfinis, C. R. Acad. Sci. Paris Sér. A 164 (1917), 88-91.

28.

S. Ulam, Scottish Book, Los Alamos, 1957.

S. M. Ulam, Adventures of a mathematician, Charles Scribner’s Sons, New York, 1976. MR 0485098

E. Zermelo, Beweis, daßjede Menge wohlgeordnet werden kann, Math. Ann. 59 (1904), no. 4, 514–516 (German). MR 1511281, DOI 10.1007/BF01445300

1.

P. Aleksandrov, Sur la puissance des ensembles measurables B, C. R. Acad. Sci. U. S. A. 162 (1916), 323-325.

2.

R. Baire, Sur les fonctions de variables réelles, Annali di Mat. Ser. III 3 (1899), 1-123.

3.

I. Bendixson, Quelques theorèmes de la théorie des ensembles de points, Acta Math. 2 (1883), 415-429. MR 1554609

4.

D. Blackwell, Infinite games and analytic sets, Proc. Nat. Acad. Sci. U. S. A. 58 (1967), 1836-1837. MR 221466

5.

E. Borel, Leçons sur la théorie des fonctions, Gauthier-Villars, Paris, 1898.

6.

E. Borel, Leçons sur les fonctions de variables réelles, Gauthier-Villars, Paris, 1905.

7.

P. Cohen, The independence of the continuum hypothesis. I, II, Proc. Nat. Acad. Sci. U. S. A. 50 (1963), 1143-1148; 51 (1964), 105-110. MR 157890

8.

S. Feferman and A. Lévy, Independence results in set theory by Cohen's method. II, Notices Amer. Math. Soc. 10 (1963), 593.

9.

D. Gale and F. Stewart, Infinite games with perfect information, Ann. of Math. Studies, no. 28, Princeton Univ. Press, Princeton, N. J., 1953, pp. 245-266. MR 54922

10.

K. Gödel, Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. I, Monatshefte f. Math. u. Physik 38 (1931), 173-198. MR 1549910

11.

K. Gödel, The consistency of the axiom of choice and of the generalized continuum hypothesis, Proc. Nat. Acad. Sci. U. S. A. 24 (1938), 556-557.

12.

L. Harrington, Analytic determinacy and O^#, J. Symbolic Logic 43 (1978), 685-693. MR 518675

13.

F. Hausdorff, Die Mächtigkeit der Borelschen Mengen, Math. Ann. 77 (1916), 430-437. MR 1511869

14.

S. Kleene, Introduction to metamathematics, Van Nostrand, New York, 1955. MR 51790

15.

M. Kondô, Sur l'uniformisation des complémentaires analytiques et les ensembles projectifs de la seconde class, Japan J. Math. 15 (1938), 197-230.

16.

H. Lebesgue, Intégrale, longuer, aire, Thèse, Paris, 1902.

17.

H. Lebesgue, Sur les fonctions représentables analytiquement, Journal de Math. Sér. 6 1 (1905), 139-216.

18.

D. A. Martin, Measurable cardinals and analytic games, Fund. Math. 66 (1970), 287-291. MR 258637

19.

D. A. Martin, Borel determinacy, Ann. of Math. (2) 102 (1975), 363-371. MR 403976

20.

D. A. Martin, Infinite games, Proc. Internat. Congr. Mathematicians (Helsinki, 1978), Accad. Sci. Fenn., Helsinki, 1980. MR 562614

21.

D. A. Martin, Projective sets and cardinal numbers, J. Symbolic Logic (to appear). MR 177887

22.

J. Mycielski and H. Steinhaus, A mathematical axiom contradicting the axiom of choice, Bull. Acad. Polon. Sci. 10 (1962), 1-3. MR 140430

23.

J. Mycielski and S. Swierczkowski, On the Lebesgue measurability and the axiom of determinateness, Fund. Math. 54 (1964), 67-71. MR 161788

24.

W. Sierpiński, Les ensembles projectifs et analytiques, Mémorial des Sciences Mathématiques 112, Gauthier-Villars, Paris, 1950 MR 52484

25.

J. Silver, Counting the number of equivalence classes of Borel and analytic equivalence relations, Ann. of Math. Logic 18 (1980), 1-28. MR 568914

26.

R. Solovay, A model of set theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1-56. MR 265151

27.

M. Suslin, Sur une définition des ensembles measurables B sans nombres transfinis, C. R. Acad. Sci. Paris Sér. A 164 (1917), 88-91.

28.

S. Ulam, Scottish Book, Los Alamos, 1957.

29.

S. Ulam, Adventures of a mathematician, Charles Scribner & Sons, New York, 1976. MR 485098

30.

E. Zermelo, Beweis, doss jede Menge wohlgeordnet werden kann, Math. Ann. 59 (1904), 514-516. MR 1511281