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A remark on Gödel’s incompleteness theorems

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Il Nuovo Cimento B (1971-1996)

Summary

If a logico-mathematical system L is such that the set of the permitted propertiesP(v), where v is a variable natural number, is not denumerable, the gödelization of L is clearly impossible. Now, the denumerability of this set is in reality assured only for very particular formal systems. Accordingly, Gödel’s results give solely ana posteriori proof of the actual poorness of such formal theories.

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References

  1. K. Gödel:Monatsh. Math. Phys.,38, 173 (1931). Now also in:S. Feferman et al. (Editors):Kurt Gödel — Collected Works, Vol.1 (Oxford University Press, Clarendon Press, New York, Oxford, 1986), p. 144.

    Article  MathSciNet  Google Scholar 

  2. K. Gödel:On undecidable propositions of formal mathematical systems (1934).Lecture notes inS. Feferman et al. (Editors):Kurt Gödel — Collected Works, Vol.1 (Oxford University Press, Clarendon Press, New York, Oxford, 1986), p. 346.

    Google Scholar 

  3. D. Hilbert andP. Bernays:Grundlagen der Mathematik, Vol.2 (Springer, Berlin, 1939, 19702), sect. 5.

    Google Scholar 

  4. E. Mendelson:Introduction to Mathematical Logic (Van Nostrand, Princeton, N.J., 1964), Chapts. 3, 4.

    Google Scholar 

  5. P. J. Cohen:Set Theory and the Continuum Hypothesis (Benjamin, New York, N.Y., 1966), Chapt. 1.

    Google Scholar 

  6. H. Scholz andG. Hasenjaeger:Grundzüge der mathematischen Logik (Springer, Berlin, 1961). (For the predicative systems of higher orders see Parts 4 and 5.)

    Book  Google Scholar 

  7. H. Weyl:Philosophy of Mathematics and Natural Science (Princeton University Press, Princeton, N.J., 1949, 19502), Appendix A.

    Google Scholar 

  8. Yu. Matiyasevich:Soviet Math. Dokl,11, 354 (1970).

    Google Scholar 

  9. H. Weyl:Dos Kontinuum (Veit and Co., Leipzig, 1918; Gruyter and Co., Berlin, 19322), Chapt.I, sect. 5.

    Google Scholar 

  10. J. von Neumann:Math. Z.,26, 1 (1927). Now also in: A. H. Taub (General Editor):John von Neumann — Collected Works, Vol.1 (Pergamon Press, Oxford, London, New York, Paris, 1961), p. 256.

    Article  MathSciNet  Google Scholar 

  11. A. N. Whitehead andB. Russell:Principia Mathematica, Vol.1 (Cambridge University Press, Cambridge, 1910, 19272), Chapt. II, sect. VIII of the Introduction.

    Google Scholar 

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  1. Dipartimento di Fisica dell’Universitá, Via Celoria 16, 20133, Milano, Italia

    A. Loinger

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  1. A. Loinger
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Loinger, A. A remark on Gödel’s incompleteness theorems. Nuov Cim B 108, 669–674 (1993). https://doi.org/10.1007/BF02827000

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