Abstract
Ever since Epimenides made his startling confession, philosophers and mathematicians have been fascinated by self-reference. Of course, mathematicians are not free to admit this.
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Bibliography
S. N. Artyomov. Arithmetically complete modal theories. Semiotics and Information Science,14:115â133, 1980. In Russian.
C. Bernardi. The fixed-point theorem for diagonalizable algebras. Studia Logica, 34: 239â251, 1975.
G. Boolos. The Unprovability of Consistency. Cambridge University Press, 1979. 2nd edition: The Logic of Provability, Cambridge University Press, 1995.
G. Boolos. Extremely undecidable sentences. Journal of Symbolic Logic, 47: 191â196, 1982.
H. Friedman. The disjunction property implies the numerical existence property. Proc Nat Acad Sci, 62: 2877â2878, 1975.
D. Guaspari and R. M. Solovay. Rosser sentences. Ann. Math. Logic, 16: 81â99, 1979.
D. Guaspari. Partially conservative extensions of arithmetic. Trans. AMS, 254: 47â68, 1979.
P. Hajek. On interpretability in theories containing arithmetic II Com . Math. Univ. Carol., 22: 667â688, 1982.
D. Jensen and A. Ehrenfeucht. Some problem in elementary arithmetics. Fund. Math, 92: 223â245, 1976.
G. Kreisel and G. Takeuti. Formally self-referential propo sitions in cut-free classical analysis and related systems. Diss. Math, 118: 1â50, 1974.
A. Macintyre and H. Simmons. Gödelâs diagonalization technique and related properties of theories. Colloq. Math, 28: 165â180, 1973.
F. Montagna. On the diagonalizable algebra of Peano arithmetic. Bolletino UMI (5), 16-B: 795â812, 1979.
G. Sambin. Fixed points through the finite model property. Studia Logica, 37: 287â289, 1976.
C. Smorynski. Bethâs theorem and self-referential sentences. In A. Macintyre, L. Pacholski, and J. Paris, editors, Logic Colloquium 77. North-Holland, Amsterdam, 1978.
C. Smorynski. Calculating self-referential statementsl: explicit calculations. Studia Logica, 38: 17â36, 1979.
C. Smorynski. Calculating self-referential statements. Fund Math, 109: 189â210, 1980.
C. Smorynski. Fifty years of self-reference in arithmetic. Notre Dame Journal of Formal Logic, 22: 357â374, 1981.
C. Smorynski. Commutativity and self-reference. Notre Dame Journal of Formal Logic, 213: 443â452, 1982.
C. Smorynski. Self-Reference and Modal Logic. Springer-Verlag, 1985.
C. Smorynski. An ubiquitous fixed point calculation. In L. Szczerba and K. Prazmowski, editors, Interpretability. Proceedings of the First Joint Conference on the Foundations of Mathematics Organised by the Bialystok Branch of the Warsaw University and Humboldt University (Berlin) in Doktorce 1980. Filia Uniwersytetu Warszawskiego w Bialmstoku, 1985.
R. M. Solovay. Provability interpretations of modal logic. Israel J. Math, 25: 287â304, 1976.
R. M. Solovay. On interpretability in set theory, To appear. Editorâs note: Results contained in a letter to P. Hajek, paper still not published.
V. Ć vejdar. On interpretability in set theory, To appear Editorâs note: Published as: A sentence that is difficult to interpret. Comm. Math. Univ. Carolinae. See also: Modal analysis of generalised Rosser sentences. Journal of Symbolic Logic, 48: 986â999, 1983.
A. Visser. Aspects of diagonalisation and provability. PhD thesis, University of Utrecht, 1981.
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SmoryĆski, C. (2002). Modal Logic and Self-Reference. In: Gabbay, D.M., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0466-3_1
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DOI: https://doi.org/10.1007/978-94-017-0466-3_1
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