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A note on models and submodels of arithmetic

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 255))

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References

  1. J. Robinson, Existential definability in arithmetic, Trans. Am. Math. Soc. 72 (1952).

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  2. Tarski, Contributions to the theory of models, Indg. Math. 16 (1954).

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  3. A. Robinson, Introduction to model theory and to the metamathematics of algebra, North-Holland, Amsterdam (1963).

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  4. M. Davis, H. Putnam and J. Robinson, The decision problem for exponential diophantine equations, Ann. of Math. (2) 74 (1961).

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  5. M. O. Rabin, Diophantine equations and non-standard models of arithmetic, Proceedings of the 1960 International Congress in Logic, Methodology and Philosophy of Science, Stanford University Press.

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  6. M. O. Rabin, Non standard models and the independence of the induction axiom, Essays on the foundations of mathematics dedicated to A. A. Fraenkel, The Magnes Press, Jerusalem (1961).

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  7. Solomon Feferman, Persistent and invariant formulas for outer extensions, Compositio Mathematica 20 (1968) p. 29.

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  8. Ju. V. Matijasevič, Enumerable sets are diophantine, Soviet mathematics, vol. 11, number 2 (1970). (Translated from Russian)

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Wilfrid Hodges

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© 1972 Springer-Verlag

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Gaifman, H. (1972). A note on models and submodels of arithmetic. In: Hodges, W. (eds) Conference in Mathematical Logic — London ’70. Lecture Notes in Mathematics, vol 255. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0059542

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  • DOI: https://doi.org/10.1007/BFb0059542

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05744-4

  • Online ISBN: 978-3-540-37162-5

  • eBook Packages: Springer Book Archive

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