Abstract
Robinson’s arithmetic Q is given a simple interpretation in Hájek’s weaker relational version Q H that does not use Solovay’s technique of shortening cuts. The result is placed within two research themes regarding relational arithmetics.
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Notes
- 1.
I neglect the last axiom of the ‘official’ version of Q H, which is simply a notational convention regarding the relational symbol ‘≤’. See (Švejdar 2007) for an account of how the study of relational versions of Q was initiated and (Ganea 2009; Švejdar 2009a) for the links between these theories and the theories of concatenation TC and F. It is interesting to note that the events described by Švejdar apparently had no direct connection with the Willard-Solovay correspondence regarding the link between relational theories and the second incompleteness theorem.
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Ganea, M. (2015). A Remark on a Relational Version of Robinson’s Arithmetic Q . In: Pȃrvu, I., Sandu, G., Toader, I. (eds) Romanian Studies in Philosophy of Science. Boston Studies in the Philosophy and History of Science, vol 313. Springer, Cham. https://doi.org/10.1007/978-3-319-16655-1_8
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