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Finite forcing and generic filters in arithmetic

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Part of the Lecture Notes in Mathematics book series (LNM,volume 498)

Abstract

We introduce the notions of forcing with respect to recursive function and recursive sets and forcing with respect to partial recursive function and r.e. sets. It is shown that the generic models are the same in both cases and coincide with the finitely generic model for a natural modification of arithmetic. This gives rise to a very interesting class of models which is investigated using the different ways in which it was obtained.

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References

  1. J. Barwise and A. Robinson: Completing theories by forcing, Ann. of Math. Logic 2 (1970) 119–142.

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© 1975 Springer-Verlag

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Hirschfeld, J. (1975). Finite forcing and generic filters in arithmetic. In: Saracino, D.H., Weispfenning, V.B. (eds) Model Theory and Algebra. Lecture Notes in Mathematics, vol 498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080980

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  • DOI: https://doi.org/10.1007/BFb0080980

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07538-7

  • Online ISBN: 978-3-540-38057-3

  • eBook Packages: Springer Book Archive