First-order modal logic in the necessary framework of objects

References

• Barwise, Jon. 1977. “Some Eastern Two Cardinal Theorems.” In Logic, Foundations of Mathematics, and Computability Theory, edited by Robert E. Butts and Jaakko Hintikka, 11–31. Dordrecht: D. Reidel.
   Google Scholar
• Bowen, Kenneth A. 1979. Model Theory for Modal Logic: Kripke Models for Modal Predicate Calculi. Dordrecht: D. Reidel.
   Google Scholar
• Burgess, John P. 2004. “E Pluribus Unum: Plural Logic and Set Theory.” Philosophia Mathematica 12: 193–221.
   Google Scholar
• Chang, C. C. 1965. “A Note on the Two Cardinal Problem.” Proceedings of the American Mathematical Society 16: 1148–1155.
   Web of Science ®Google Scholar
• Chang, C. C., and H. Jerome Keisler. 1990. Model Theory. 3rd ed. Amsterdam: North-Holland.
   Google Scholar
• Devlin, Keith J. 1984. Constructibility. Berlin: Springer-Verlag.
   Google Scholar
• Fine, Kit. 1977. Postscript to Worlds, Times and Selves (with A. N. Prior). London: Duckworth.
   Google Scholar
• Friedman, Harvey M.. 1999. A Complete Theory of Everything: Satisfiability in the Universal Domain. http://www.math.ohio-state.edu/~friedman/.
   Google Scholar
• Fritz, Peter. 2013. “Modal Ontology and Generalized Quantifiers.” Journal of Philosophical Logic 42: 643–678.
   Web of Science ®Google Scholar
• Fuhrken, G. 1964. “Skolem-type Normal Forms for First-order Languages with a Generalized Quantifier.” Fundamenta Mathematicae 54: 291–302.
   Google Scholar
• Hughes, G. E., and M. J. Cresswell. 1996. A New Introduction to Modal Logic. London: Routledge.
   Google Scholar
• Jensen, R. Björn 1972. “The Fine Structure of the Constructible Hierarchy.” Annals of Mathematical Logic 4: 229–308.
   Google Scholar
• Keisler, H. Jerome 1966. “First Order Properties of Pairs of Cardinals.” Bulletin of the American Mathematical Society 72: 141–144.
   Web of Science ®Google Scholar
• Koellner, Peter. 2009. “On Reflection Principles.” Annals of Pure and Applied Logic 157: 206–219.
   Web of Science ®Google Scholar
• Kreisel, Georg. 1967. “Informal Rigour and Completeness Proofs.” In Problems in the Philosophy of Mathematics, edited by Imre Lakatos, 138–186. Amsterdam: North-Holland.
   Google Scholar
• Kripke, Saul A. 1959. “A Completeness Theorem in Modal Logic.” Journal of Symbolic Logic 24: 1–14.
   Google Scholar
• Lewis, David. 1986. On the Plurality of Worlds. Oxford: Basil Blackwell.
   Google Scholar
• Mitchell, William. 1972. “Aronszajn Trees and the Independence of the Transfer Property.” Annals of Mathematical Logic 5: 21–46.
   Google Scholar
• Morley, Michael, and Robert Vaught. 1962. “Homogeneous Universal Models.” Mathematica Scandinavica 11: 37–57.
   Google Scholar
• Rayo, Agustín, and Timothy Williamson. 2003. “A Completeness Theorem for Unrestricted First-order Languages.” In Liars and Heaps: New Essays on Paradox, edited by J. C. Beall, 331–356. Oxford: Oxford University Press.
   Google Scholar
• Schmerl, James H. 1977. “An Axiomatization for a Class of Two-cardinal Models.” The Journal of Symbolic Logic 42: 174–178.
   Web of Science ®Google Scholar
• Shapiro, Stewart. 1987. “Principles of Reflection and Second-order Logic.” Journal of Philosophical Logic 16: 309–333.
   Web of Science ®Google Scholar
• Shelah, Saharon. 1979. “On Successors of Singular Cardinals.” In Logic Colloquium 78, edited by Maurice Boffa, Dirk van Dalen, and Kenneth McAloon, 357–380. Amsterdam: North-Holland.
   Google Scholar
• Shelah, Saharon. 2005. “The Pair n***0 May Fail 0-compactness.” In Logic Colloquium ’01, edited by Matthias Baaz, Sy-David Friedman, and Jan Krajíček, 402–433. Boca Raton, FL: A K Peters/CRC Press.
   Google Scholar
• Silver, Jack. 1971. “The Independence of Kurepa’s Conjecture and Two-cardinal Conjectures in Model Theory." In Axiomatic Set Theory. Proceedings of Symposia in Pure Mathematics, Volume XIII, Part I, edited by Dana S. Scott, 383–390. Providence, RI: American Mathematical Society.
   Google Scholar
• Stalnaker, Robert. 1976. “Possible Worlds.” Noûs 10: 65–75.
   Web of Science ®Google Scholar
• Tarski, Alfred. 2002 [1936]. “On the Concept of Following Logically.” History and Philosophy of Logic 23 :155–196. Originally published in Polish and German in 1936.
   Web of Science ®Google Scholar
• Vaught, R. L. 1964. “The Completeness of Logic with the Added Quantifier ‘There are Uncountably Many’.” Fundamenta Mathematicae 54: 303–304.
   Google Scholar
• Vaught, R. L. 1965a. “A Löwenheim--Skolem Theorem for Cardinals for Apart.” In The Theory of Models, edited by J. W. Addison, L. Henkin, and A. Tarski, 390–401. Amsterdam: North-Holland.
   Google Scholar
• Vaught, R. L. 1965b. “The Löwenheim--Skolem Theorem.” In Methodology Logic and Philosophy of Science, edited by Yehoshua Bar-Hillel, 81–89. Amsterdam: North-Holland.
   Google Scholar
• Williamson, Timothy. 2000a. “Existence and Contingency.” Proceedings of the Aristotelian Society 100: 321–343.
   Google Scholar
• Williamson, Timothy. 2000b. “The Necessary Framework of Objects.” Topoi 19: 201–208.
   Web of Science ®Google Scholar
• Williamson, Timothy. 2003. “Everything.” Philosophical Perspectives 17: 415–465.
   Google Scholar
• Williamson, Timothy. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press.
   Google Scholar