Notre Dame Journal of Formal Logic

Arithmetic with Satisfaction

James Cain

Abstract

A language in which we can express arithmetic and which contains its own satisfaction predicate (in the style of Kripke's theory of truth) can be formulated using just two nonlogical primitives: $'$ (the successor function) and Sat (a satisfaction predicate).

Article information

Source
Notre Dame J. Formal Logic, Volume 36, Number 2 (1995), 299-303.

Dates
First available in Project Euclid: 18 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1040248460

Digital Object Identifier
doi:10.1305/ndjfl/1040248460

Mathematical Reviews number (MathSciNet)
MR1345750

Zentralblatt MATH identifier
0837.03044

Subjects
Primary: 03F30: First-order arithmetic and fragments
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35] 03C62: Models of arithmetic and set theory [See also 03Hxx]

Citation

Cain, James. Arithmetic with Satisfaction. Notre Dame J. Formal Logic 36 (1995), no. 2, 299--303. doi:10.1305/ndjfl/1040248460. https://projecteuclid.org/euclid.ndjfl/1040248460


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References

  • Kripke, S., “Outline of a Theory of Truth,” Journal of Philosophy, vol. 72 (1975), pp. 690–716. Zbl 0952.03513
  • Visser, A., “Semantics and the Liar Paradox,” pp. 617–706 in Handbook of Philosophical Logic, vol. 4, edited by D. Gabbay and F. Guenthner, Reidel, Dordrecht, 1983. Zbl 0875.03030