Provability, Computability and Reflection available in Hardcover
- Pub. Date:
- Elsevier Science
These two volumes cover the principal approaches to constructivism in mathematics. They present a thorough, up-to-date introduction to the metamathematics of constructive mathematics, paying special attention to Intuitionism, Markov's constructivism and Martin-Lof's type theory with its operational semantics. A detailed exposition of the basic features of constructive mathematics, with illustrations from analysis, algebra and topology, is provided, with due attention to the metamathematical aspects. Volume 1 is a self-contained introduction to the practice and foundations of constructivism, and does not require specialized knowledge beyond basic mathematical logic. Volume 2 contains mainly advanced topics of a proof-theoretical and semantical nature.
|Series:||Studies in Logic and the Foundations of Mathematics Series , #1|
|Product dimensions:||6.14(w) x 9.21(h) x 0.94(d)|
Table of Contents7. The Topology of Metric Spaces. 8. Algebra. 9. Finite Type Arithmetic and Theories of Operators. 10. Proof Theory of Intuitionistic Logic. 11. The Theory of Types and Constructive Set Theory. 12. Choice Sequences. 13. Semantical Completeness. 14. Sheaves, Sites and Higher Order Logic. 15. Applications of Sheaf Models. 16. Epilogue.