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Set TheoryBoolean-Valued Models and Independence Proofs$

John L. Bell

Print publication date: 2005

Print ISBN-13: 9780198568520

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198568520.001.0001

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Set Theory
Oxford University Press

Bibliography references:

Balbes, R. and Dwinger, P. (1974). Distributive Lattices. University of Missouri Press, Columbia, Missouri.

Banaschewski, B. and Bhutani, L. (1986). Boolean algebras in a localic topos. Math. Proc. Camb. Philos. Soc. 100 (1), 43–55.

Banaschewski, B. and Brümmer, G. (1986). Thoughts on the Cantor–Bernstein theorem. Quaestiones Math. 9 (1–4), 1–27.

Bell, J. L. (1975). A characterization of complete Boolean algebras. J. London Math. Soc. 12 (2), 86–88.

Bell, J. L. (1976). Uncountable Standard models of ZFC+VL. Set Theory and Hierarchy Theory: A Memorial Tribute to A. Mostowski, Birutowice, Poland 1975. Lecture Notes in Mathematics, vol. 537, Springer, Berlin–Heidelberg–New York.

Bell, J. L. (1976a). A note on generic ultrafilters. Z. Math. Logik 22, 307–310.

Bell, J. L. (1981). Isomorphism of structures in S-toposes. J. Symbolic Logic 46(3), 449–459.

Bell, J. L. (1983). On the strength of the Sikorski extension theorem for Boolean algebras. J. Symbolic Logic 48 (3), 841–846.

Bell, J. L. (1988). Toposes and Local Set Theories: An Introduction. Oxford Logic Guides 14. Clarendon Press, Oxford.

Bell, J. L. (1997). Zorn's lemma and complete Boolean algebras in intuitionistic type theories. J. Symbolic Logic 62 (4), 1265–1279.

Bell, J. L. (1999). Boolean algebras and distributive lattices treated constructively. Math. Logic Quart. 45, 135–143.

Bell, J. L. and Machover, M. (1977). A Course in Mathematical Logic. North-Holland, Amsterdam.

Cohen, P. J. (1963). The independence of the continuum hypothesis I. Proc. Nat. Acad. Sci. USA 50, 1143–1148.

Cohen, P. J. (1964). The independence of the continuum hypothesis II. Proc. Nat. Acad. Sci. USA 51, 105–110.

Cohen, P. J. (1966). Set Theory and the Continuum Hypothesis. Benjamin, New York.

Davis, M. (1977). A relativity principle in quantum mechanics. Int. J. Theor. Phys. 16, 867–874.

Devlin, K. J. (1977). Constructibility. In J. Barwise, ed., Handbook of Mathematical Logic. North-Holland, Amsterdam.

Devlin, K. J. and Johnsbraten, H. (1974). The Souslin Problem. Lecture Notes in Mathematics, vol. 405, Springer, Berlin–Heidelberg–New York.

(p.185) Diaconescu, R. (1975a). Axiom of choice and complementation. Proc. Amer. Math. Soc. 51, 176–178.

Dickmann, M. (1975). Large Infinitary Languages. North-Holland, Amsterdam.

Drake, F. R. (1974). Set Theory: An Introduction to Large Cardinals. North-Holland, Amsterdam.

Easton, W. B. (1970). Powers of regular cardinals. Ann. Math. Logic 1, 141–178.

Ellentuck, E. (1976). Categoricity regained. J. Symbolic Logic 41, 639–643.

Feferman, S. (1965). Some applications of the notions of forcing and generic sets. Fund. Math. 56 325–345.

Felgner, U. (1971). Models of ZF-set Theory. Lecture Notes in Mathematics, vol. 223, Springer, Berlin–Heidelberg–New York.

Fitting, M. C. (1969). Intuitionistic Logic, Model Theory and Forcing. North-Holland, Amsterdam.

Fourman, M. P. and Hyland, J. M. E. (1979). Sheaf models for analysis. In Fourman Mulvey and Scott eds. (1979), pp. 280–302.

Fourman, M. P. and Scott, D. S. (1979). Sheaves and logic. In Fourman Mulvey and Scott eds. (1979), pp. 302–401.

Fourman, M. P, Mulvey, C. J., and Scott, D. S. eds. (1979). Applications of Sheaves. Proc. L.M.S. Durham Symposium 1977. Lecture Notes in Mathematics, vol. 753, Springer, Berlin–Heidelberg–New York.

Goldblatt, R. I. (1979). Topoi: The Categorical Analysis of Logic. North-Holland, Amsterdam.

Goodman, N. and Myhill, J. (1978). Choice implies excluded middle. Z. Math. Logik Grundlag. Math. 24 (5), 461.

Grayson, R. J. (1975). A sheaf approach to models of set theory. M.Sc. thesis, Oxford University.

Grayson, R. J. (1978). Intuitionistic set theory. D. Phil. Thesis, Oxford University.

Grayson, R. J. (1979). Heyting-valued models for intuitionistic set theory. In Fourman Mulvey and Scott eds. (1979), pp. 402–414.

Grigorieff, S. (1975). Intermediate submodels and generic extensions in set theory. Ann. Math. 101, 447–490.

Halmos, P. R. (1963). Lectures on Boolean Algebras. Van Nostrand, New York.

Halmos, P. R. (1965). Measure Theory. Van Nostrand, New York.

Higgs, D. (1973). A category approach to Boolean-valued set theory. (Unpublished typescript, University of Waterloo.)

Jauch, J. M. (1968). Foundations of Quantum Mechanics Addison-Wesley, Reading, MA.

Jech, T. J. (1967). Non-provability of Souslin's hypothesis. Comment. Math. Univ. Carolinae 8, 291–305.

Jech, T. J. (1971). Lectures in Set Theory. Lecture Notes in Mathematics, vol. 217, Springer, Berlin–Heidelberg–New York.

Jech, T. J. (1973). The Axiom of Choice. North-Holland, Amsterdam.

(p.186) Jech, T. J., ed. (1974). Axiomatic Set Theory. AMS Proceedings of Symosia in Pure Mathematics, vol. XIII, Part II. American Mathematical Society, Providence.

Johnstone, P. T. (1977). Topos Theory. Academic Press, London.

Johnstone, P. T. (1982). Stone Spaces. Cambridge Studies in Advanced Mathematics 3. Cambridge University Press, Cambridge.

Johnstone, P. T. (2002). Sketches of an Elephant: A Topos Theory Compendium, vols. I and II. Oxford Logic Guides vols. 43 and 44, Clarendon Press, Oxford.

Kelley, J. L. (1955). General Topology. Van Nostrand, New York.

Kripke, S. (1967). An extension of a theorem of Gaifman-Hales-Solovay. Fund. Math. 61, 29–32.

Kunen, K. (1980). Set Theory. North-Holland, Amsterdam.

Lambek, J. and Scott, P. J. (1986). Introduction to Higher-Order Categorical Logic. Cambridge University Press, Cambridge.

Lawvere, F. W. (1971). Quantifiers and sheaves. In Actes du Congrès Intern. Des. Math. Nice 1970, tome I. Gauthier-Villars, Paris, pp. 329–334.

Levy, A. (1965). Definability in axiomatic set theory I. Proceedings of the 1964 International Congress on Logic, Methodology and Philosophy of Science. North-Holland, Amsterdam.

Levy, A. and Solovay, R. M. (1967). Measurable cardinals and the continuum hypothesis. Israel J. Math. 5, 234–238.

Mac Lane, S. (1971). Categories for the Working Mathematician. Springer-Verlag, Berlin.

Mac Lane, S. (1975). Sets, topoi, and internal logic in categories. In H. E. Rose and J. C. Shepherdson, eds., Logic Colloquium 73, pp. 119–134. North-Holland, Amsterdam.

Mac Lane, S. and Moerdijk, I. (1992). Sheaves in Geometry and Logic: A First Introduction to Topos Theory. Springer-Verlag, Berlin

Martin, D. A. and Solovay, R. M. (1967). Internal Cohen extensions. Ann. Math. Logic 2, 143–178.

McLarty, C. (1992). Elementary Categories, Elementary Toposes. Oxford University Press, Oxford.

Miller, E. W. (1943). A note on Souslin's problem. Amer. J. Math. 65, 673–678.

Mitchell, W. (1972). Boolean topoi and the theory of sets. J. Pure Appl. Algebra 2, 261–274.

Osius, G. (1974a). Categorical Set Theory: a characterization of the category of sets. J. Pure Appl. Algebra 4, 79–119.

Rasiowa, H. and Sikorski, R. (1963). The Mathematics of Metamathematics. PWN, Warsaw.

Rosser, J. B. (1969). Simplified Independence Proofs: Boolean-Valued Models of Set Theory. Academic Press, New York.

Rudin, M. E. (1977). Martin's Axiom. In J. Barwise, ed., Handbook of Mathematical Logic. North-Holland, Amsterdam.

(p.187) Scott, D. S. (1967). Boolean-Valued Models for Set Theory. Mimeographed notes for the 1967 American Math. Soc. Symposium on axiomatic set theory.

Scott, D. S. (1968). Extending the topological interpretation to intuitionistic analysis I. Compositio Math. 20, 194–210.

Scott, D. S. (1969). Boolean-valued models and non-standard analysis. Applications of Model Theory to Analysis, Algebra and Probability. Holt, Reinhart and Winston, New York.

Scott, D. S. (1970). Extending the topological interpretation to intuitionistic analysis II. In A. Kino, J. Myhill, and R. E. Vesley, eds., Intuitionism and Proof Theory, pp. 235–256. North-Holland, Amsterdam.

Scott, D. S., ed. (1971). Axiomatic Set Theory. AMS Proceedings of Symosia in Pure Mathematics, vol. XIII, Part I. American Mathematical Society, Providence.

Shoenfield, J. R. (1971). Unramified forcing. In Scott, ed. (1971).

Sikorski, R. (1964). Boolean Algebras. Springer, Berlin–Heidelberg–New York.

Solovay, R. M. (1965). 20 can be anything it ought to be. In J. W. Addison, L. Henkin, and A. Tarski, eds., The Theory of Models. North-Holland, Amsterdam.

Solovay, R. M. (1966). New proof of a theorem of Gaifman and Hales. Bull. Amer. Math. Soc. 72, 282–284.

Solovay, R. M. (1970). A model of set theory in which every set of reals is Lebesgue measurable. Ann. Math. 92, 1–56.

Solovay, R. M. and Tennenbaum, S. (1971). Iterated Cohen extensions and Souslin's problem. Ann. Math. 94, 201–245.

Takeuti, G. (1978). Two Applications of Logic to Mathematics. Princeton University Press, Princeton.

Takeuti, G. and Zaring, W. M. (1973). Axiomatic Set Theory. Berlin–Heidelberg–New York.

Tennenbaum, S. (1968). Souslin's problem. Proc. Nat. Acad. Sci. USA 59, 60–63.

Tierney, M. (1972). Sheaf theory and the continuum hypothesis. In F. W. Lawvere, ed., Toposes, Algebraic Geometry and Logic. Springer Lecture Notes in Math. 274, pp. 13–42.

Vopěnka, P. (1965). The limits of sheaves and applications on construction of models. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astron. Phys. 13 189–192.

Vopěnka, P. (1967). General theory of -models. Comment. Math. Univ. 8, 145–170.

Vopěnka, P. and Hajek, P. (1972). The Theory of Semisets. North-Holland, Amsterdam.