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    • Publisher:
      Cambridge University Press
      Publication date:
      March 2017
      March 2017
      ISBN:
      9781316717219
      9781107168350
      DOI:
      https://doi.org/10.1017/9781316717219
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.85kg, 438 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
      Series:
      Perspectives in Logic (6)
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    • Selected: Digital
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    Subjects:
    Mathematics, Logic, Categories and Sets, Computer Science, Programming Languages and Applied Logic
    Series:
    Perspectives in Logic (6)
    Information

    Book description

    Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the Lα-hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the Jα-hierarchy and the Jensen 'fine-structure theory'.

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    Contents

    Contents
    References
    Bibliography
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    Beller, A., Litman, A. 1980 A Strengthening of Jensen's □ Principles. J. Symbolic Logic 45, 251–264
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    Devlin, K. J. 1973 Aspects of Constructibility. Springer-Verlag: Lecture Notes in Mathematics 354
    Devlin, K. J. 1979 Fundamentals of Contemporary Set Theory. Springer-Verlag
    Devlin, K. J. 1979a Variations on ◊. J. Symbolic Logic 44, 51–58
    Devlin, K. J., Jensen, R. B. 1975 Marginalia to a Theorem of Silver. In “Logic Conference Kiel 1974”. Springer- Verlag: Lecture Notes in Mathematics 499, 115–142
    Devlin, K. J., Johnbråten, H. 1974 The Souslin Problem. Springer-Verlag: Lecture Notes in Mathematics 405
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    Lévy, A. 1957 Indépendence Conditionnelle de V = L et d'Axiomes qui se Rattachent au Systeme de M. Gödel. C.R. Acad. Sci. Paris 245, 1582–1583
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    Mitchell, W. 1972 Aronszajn Trees and the Independence of the Transfer Property. Annals Math. Logic 5, 21–46
    Montague, R. M. 1961 Fraenkel's Addition to the Axioms of Zermelo. In “Essays on the Foundations of Mathematics” (ed. Bar-Hillel, Y. et al.). The Magnes Press (Jerusalem), 91–114
    Morley, M., Vaught, R. 1962 Homogeneous Universal Models. Math. Scand. 11, 37–57
    Mostowski, A. 1949 An Undecidable Arithmetical Statement. Fund. Math. 36, 143–164
    Platek, R. 1966 Foundations of Recursion Theory. PhD thesis, Stanford University
    Prikry, K. L., Solovay, R. M. 1975 On Partitions into Stationary Sets. J. Symbolic Logic 40, 75–80
    Rowbottom, F. 1971 Some Strong Axioms of Infinity Incompatible with the Axiom of Constructibility. Ann. of Math. Logic 3, 1–44
    Shelah, S., Stanley, L. J. 1983 S-Forcing, I: A “Black Box” Theorem for Morasses
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    Silver, J. H. 1971 Some Applications of Model Theory in Set Theory. Ann. of Math. Logic 3, 45–110
    Silver, J. H. 1971a The Independence of Kurepa's Conjecture and Two-Cardinal Conjectures in Model Theory. In “Axiomatic Set Theory”, proc. Symp. in Pure Math. 13 (ed. Scott, D.), Amer. Math. Soc. 383–390
    Solovay, R. M. 1967 A Nonstructible Δ13 Set of Integers. Trans. Amer. Math. Soc. 127, 50–75
    Solovay, R. M., Tennenbaum, S. 1971 Iterated Cohen Extensions and Souslin's Problem. Ann. of Math. 94, 201–245
    Souslin, M. 1920 Problème 3. Fund. Math. 1, 223
    Stanley, L. J. 1975 L-Like Models of Set Theory: Forcing, Combinatorial Principles, and Morasses. PhD Thesis (Berkeley)
    Todorcevic, S. 1983 Trees and Linearly Ordered Sets. In “Topology Handbook”
    Velleman, D. 1984 Simplified Morasses. J. Symbolic Logic
    Velleman, D. 1984a Simplified Morasses with Linear Limits. J. Symbolic Logic

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