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Existentially closed structures and Gödel's second incompleteness theorem

  • Zofia Adamowicz (a1) and Teresa Bigorajska (a2)

We prove that any 1-closed (see def 1.1) model of the Π2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Gödel incompleteness theorem without the use of the Gödel diagonal lemma. We prove a few other theorems by the same method.

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[1]Adamowicz Z. and Zbierski P., Logic of mathematics, John Wiley & Sons, 1997.
[2]Boolos G., A new proof of the Gödel incompleteness theorem, Notices of the American Mathematical Society, vol. 36 (1989), pp. 388390.
[3]Cieślinski C., Gödels incompleteness theorems and semantical antinomies, Ph.D. thesis, Warsaw University, 1999.
[4]Dimtrakopoulos K., Overspill and fragments of arithmetic, Archive of Mathematical Logic, vol. 28 (1989), pp. 173179.
[5]Hodges W., Model theory, Encyclopedia of Mathematics an its Applications, no. 42, Cambridge University press, 1993.
[6]Jech T., On Gödel second incompleteness theorem, Proceedings of the American Mathematical Society, vol. 121 (1994), no. 1, pp. 311313.
[7]Kikuchi M., A note on boolos' proof of the incompleteness theorem, Mathematical Logic Quaterly, vol. 40 (1994), pp. 528532.
[8]Kikuchi M., Kolmogorov complexity and the second incompleteness theorem, Archive of Mathematical Logic, vol. 36 (1997), pp. 437443.
[9]Kotlarski H., On the incompleteness theorems, this Journal, vol. 59 (1994), no. 4, pp. 14141419.
[10]Kotlarski H., An addition to rosser's theorem, this Journal, vol. 61 (1996), pp. 285292.
[11]Kotlarski H., Other proofs of old results, Mathematical Logic Quarterly, vol. 44 (1998), pp. 474480.
[12]Smorynski C., The incompleteness theorem, (J. Barwise, editor), Handbook of Mathematical Logic, North Holland Publishing Company, Amsterdam, 1977, pp. 821865.
[13]Vopenka P., A new proof of the Gödel's result of non-provability of consistency, L'Académie Polonaise des Sciences. Bulletin. Série des Sciences Mathématiques, vol. 14 (1966), pp. 111116.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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