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Book Review
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Book Information
Author(s):
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
References:
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- 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
Additional Information:
Reviewer(s):
Thomas
Jech
Review Information:
Journal:
Bull. Amer. Math. Soc.
5
(1981),
339-349.
DOI:
10.1090/S0273-0979-1981-14952-1
PII:
S 0273-0979(1981)14952-1
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