Abstract
In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over \( PA \). Let \({\mathfrak {Th}}\) denote the class of models of \( PA \) which admit an expansion to a model of theory \({ Th}\). We show (combining some well known results and original ideas) that
where \({\mathfrak {PA}}\) denotes simply the class of all models of \( PA \) and \({\mathfrak {RS}}\) denotes the class of recursively saturated models of \( PA \). Our main original result is that every model of \( PA \) which admits an expansion to a model of \( CT ^-\), admits also an expansion to a model of \( UTB \). Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that \( UTB \) is not relatively interpretable in \( TB \), thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010).
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Acknowledgements
Funding was provided by National Science Centre in Cracow (NCN) (Grant No. DEC-2011/01/B/HS1/03910).
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Łełyk, M., Wcisło, B. Models of weak theories of truth. Arch. Math. Logic 56, 453–474 (2017). https://doi.org/10.1007/s00153-017-0531-1
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DOI: https://doi.org/10.1007/s00153-017-0531-1