Kolmogorov's ideas in the theory of operations on sets

CONTENTS Foreword Introduction § 1. Introduction to the theory of operations on sets § 2. The Kolmogorov hierarchy § 3. The R-transform § 4. Inductive analysis. Indices § 5. R-sets: construction of the hierarchy § 6. The nature of R-sets § 7. Properties of R-sets § 8. Kolmogorov's problem on the lengths of Borel hierarchies Conclusion References

[1]  H. Lebesgue.  Sur les fonctions representables analytiquement , 1905 .

[2]  Paul Alexandroff.  Sur la puissance des ensembles mesurables B 162 , .

[3]  Michel Souslin.  Sur une definition des ensembles mesurables B sans nombres transfinis , 1917 .

[4]  Sur les ensembles complémentaires aux ensembles (A) , 1924 .

[5]  Wacław Sierpiński,et al.  Leçons sur les ensembles analytiques et leurs applications , 1930 .

[6]  L. Kantorovitch,et al.  Memoir on the Analytical Operations and Projective Sets (II) , 1932 .

[7]  P. Wolfe.  The strict determinateness of certain infinite game , 1955 .

[8]  S. Ulam.  A collection of mathematical problems , 1960 .

[9]  P. S. ALEKSANDROV AND THE THEORY OF δs-OPERATIONS , 1966 .

[10]  Peter G. Hinman.  HIERARCHIES OF EFFECTIVE DESCRIPTIVE SET THEORY , 1969 .

[11]  The finite levels of the hierarchy of effective R-sets , 1973 .

[12]  Yiannis N. Moschovakis,et al.  Elementary induction on abstract structures , 1974 .

[13]  J. Fenstad,et al.  ON ABSOLUTELY MEASURABLE SETS , 1974 .

[14]  Stål Aanderaa.  Inductive Definitions and Their Closure Ordinals , 1974 .

[15]  R. Vaught.  Invariant sets in topology and logic , 1974 .

[16]  M. M. Choban.  Operations over sets , 1975 .

[17]  Peter Aczel.  Quantifiers; Games and Inductive Definitions , 1975 .

[18]  John P. Burgess,et al.  Remarks on invariant descriptive set theory , 1975 .

[19]  Leo Harrington,et al.  On monotone vs. nonmonotone induction , 1976 .

[20]  Peter Aczel,et al.  An Introduction to Inductive Definitions , 1977 .

[21]  Yiannis N. Moschovakis,et al.  Recursion in Higher Types , 1977 .

[22]  Donald A. Martin,et al.  Descriptive Set Theory: Projective Sets , 1977 .

[23]  Alexander S. Kechris,et al.  Spector Second Order Classes and Reflection , 1978 .

[24]  D. Blackwell.  Borel-Programmable Functions , 1978 .

[25]  Y. Katznelson,et al.  On αβ-sets , 1979 .

[26]  Arnorld W. Miller.  On the length of Borel hierarchies , 1979 .

[27]  Y. Moschovakis.  Descriptive Set Theory , 1980 .

[28]  J. R. Burgess.  What are R-Sets? , 1982 .

[29]  J. Burgess.  Classical hierarchies from a modern standpoint. Part I. C-sets , 1983 .

[30]  R. Vaught,et al.  Borel games and the Baire property , 1983 .

[31]  John P. Burgess,et al.  Classical hierarchies form a modern standpoint. Part III. BP-sets , 1983 .

[32]  Chris Freiling.  Banach Games , 1984, J. Symb. Log..

[33]  Jon Marks,et al.  On the Classification of Homo , 1984, Current Anthropology.

[34]  R. Barua.  R-SETS AND CATEGORY , 1984 .

[35]  V. Uspenskii.  NIKOLAI NIKOLAEVICH LUZIN: Luzin's contribution to the descriptive theory of sets and functions: concepts, problems, predictions , 1985 .

[36]  V. Kanovei.  NIKOLAI NIKOLAEVICH LUZIN: The development of the descriptive theory of sets under the influence of the work of Luzin , 1985 .

[37]  V. Kanovei.  The axiom of determinacy and the modern development of descriptive set theory , 1988 .