E-Book Overview
This monograph is a follow up to the author's classic text Boolean-Valued Models and Independence Proofs in Set Theory, providing an exposition of some of the most important results in set theory obtained in the 20th century-the independence of the continuum hypothesis and the axiom of choice. Aimed at research students and academics in mathematics, mathematical logic, philosophy, and computer science, the text has been extensively updated with expanded introductory material, new chapters and a new appendix on category theory, and includes recent developments in the field. Numerous exercises, along with the enlarged and entirely updated background material, make this an ideal text for students in logic and set theory.
E-Book Content
OX FO R D L O G I C G U I D ES : 4 7 General Editors ANGUS MACINTYRE DOV M. GABBAY DANA SCOTT OXFORD LOGIC GUIDES 10. 17. 18. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. Michael Hallett: Cantorian set theory and limitation of size Stewart Shapiro: Foundations without foundationalism John P. Cleave: A study of logics C. McLarty: Elementary categories, elementary toposes R.M. Smullyan: Recursion theory for metamathematics Peter Clote and Jan Kraj´ıcek: Arithmetic, proof theory, and computational complexity A. Tarski: Introduction to logic and to the methodology of deductive sciences G. Malinowski: Many valued logics Alexandre Borovik and Ali Nesin: Groups of finite Morley rank R.M. Smullyan: Diagonalization and self-reference Dov M. Gabbay, Ian Hodkinson, and Mark Reynolds: Temporal logic: Mathematical foundations and computational aspects, volume 1 Saharon Shelah: Cardinal arithmetic Erik Sandewall: Features and fluents: Volume I: A systematic approach to the representation of knowledge about dynamical systems T.E. Forster: Set theory with a universal s