论文信息 - A Theory of Formal Truth Arithmetically Equivalent to ID1

A Theory of Formal Truth Arithmetically Equivalent to ID1

We present a theory VF of partial truth over Peano arithmetic and we prove that VF and ID 1 , have the same arithmetical content. The semantics of VF is inspired by van Fraassen's notion of supervaluation.

Andrea Cantini

[1] Jon Barwise,et al. Admissible sets and structures , 1975 .

[2] Ray Turner,et al. A theory of properties , 1987, Journal of Symbolic Logic.

[3] Harvey M. Friedman,et al. An axiomatic approach to self-referential truth , 1987, Ann. Pure Appl. Log..

[4] Saul A. Kripke,et al. Outline of a Theory of Truth , 1975 .

[5] Gerhard Jäger,et al. Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen Zahlen , 1980, Arch. Math. Log..

[6] Andrea Cantini,et al. Notes on Formal Theories of Truth , 1989, Math. Log. Q..

[7] Albert Visser,et al. Four valued semantics and the Liar , 1984, J. Philos. Log..

[8] Solomon Feferman,et al. Reflecting on incompleteness , 1991, Journal of Symbolic Logic.

[9] Jr. Hartley Rogers. Theory of Recursive Functions and Effective Computability , 1969 .

[10] Melvin Fitting. Partial Models and Logic Programming , 1986, Theor. Comput. Sci..

[11] Donald Perlis,et al. Languages With Self-Reference I: Foundations , 1985, Artif. Intell..

[12] H. Schwichtenberg. Proof Theory: Some Applications of Cut-Elimination , 1977 .

[13] William N. Reinhardt. Some remarks on extending and interpreting theories with a partial predicate for truth , 1986, J. Philos. Log..

[14] Peter W. Woodruff. Paradox, truth and logic part I: Paradox and truth , 1984, J. Philos. Log..

[15] John P. Burgess,et al. The truth is never simple , 1986, Journal of Symbolic Logic.