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
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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
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