Hostname: page-component-77c89778f8-5wvtr Total loading time: 0 Render date: 2024-07-18T23:22:12.690Z Has data issue: false hasContentIssue false

A theory of formal truth arithmetically equivalent to ID1

Published online by Cambridge University Press:  12 March 2014

Andrea Cantini*
Affiliation:
Dipartimento di Filosofia, Università di Firenze, 1-50139 Firenze, Italy

Abstract

We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID1, have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1990

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Barwise, J., Admissible sets and structures, Springer-Verlag, Berlin, 1975.CrossRefGoogle Scholar
[2]Burgess, J., The truth is never simple, this Journal, vol. 51 (1986), pp. 663681.Google Scholar
[3]Cartini, A., Tarski extensions of theories, Atti delconvegno nazionale dilogica (Bernini, S., editor), Bibliopolis, Napoli, 1982, pp. 219237.Google Scholar
[4]Cartini, A., Notes on formal theories of truth, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 35 (1989), pp. 99130.Google Scholar
[5]Feferman, S., Gödel's incompleteness theorems and the reflective closure of theories, 33 pages (unpublished).Google Scholar
[6]Feferman, S., Reflecting on incompleteness, handwritten notes (39 pages), 03 1987.Google Scholar
[7]Feferman, S. and Sieg, W., Iterated inductive definitions and subsystems of analysis, Iterated inductive definitions and subsystems of analysis: recent proof-theoretical studies, Lecture Notes in Mathematics, vol. 897, Springer-Verlag, Berlin, 1981, pp. 17142.Google Scholar
[8]Fitting, M., Partial models and logic programming, Theoretical Computer Science, vol. 48 (1986), pp. 229255.CrossRefGoogle Scholar
[9]Friedman, H. and Sheard, M., An axiomatic approach to self-referential truth, Annals of Pure and Applied Logic, vol. 33 (1987), pp. 121.CrossRefGoogle Scholar
[10]Jäger, G., Zur Beweistheorie der Kripke-Platek Mengenlehre, Archiv für Mathematische Logik und Grundlagenforschung, vol. 22 (1982), pp. 121139.CrossRefGoogle Scholar
[11]Kripke, S., Outline of a theory of truth, Journal of Philosophy, vol. 72 (1975), pp. 690716.CrossRefGoogle Scholar
[12]Lolli, G., Logic(s) for computer science, Topics and perspectives of contemporary logic and philosophy of science (to appear).Google Scholar
[13]Perlis, D., Languages with self-reference. I: Foundations, Artificial Intelligence, vol. 25 (1985), pp. 301323.CrossRefGoogle Scholar
[14]Reinhardt, W., Some remarks on extending and interpreting theories with a partial predicate for truth, Journal of Philosophical Logic, vol. 15 (1986), pp. 219251.CrossRefGoogle Scholar
[15]Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
[16]Schwichtenberg, H., Proof theory: some applications of cut-elimination, Handbook of mathematical logic (Barwise, J., editor), North-Holland, Amsterdam, 1977, pp. 867895.CrossRefGoogle Scholar
[17]Spector, C., Inductively defined sets of numbers, Infinitistic methods, Pergamon Press, Oxford, 1961, pp. 97102.Google Scholar
[18]Turner, R., A theory of properties, this Journal, vol. 52 (1987), pp. 455471.Google Scholar
[19]van Fraassen, B., Formal semantics, Macmillan, New York, 1971.Google Scholar
[20]Visser, A., Four-valued semantics and the Liar, Journal of Philosophical Logic, vol. 13 (1984), pp. 181212.CrossRefGoogle Scholar
[21]Woodruff, P., Paradox, truth and logic. I: paradox and truth, Journal of Philosophical Logic, vol. 13 (1984), pp. 867896.CrossRefGoogle Scholar