Abstract
In earlier work we introduced two systems for nonstandard analysis, one based on classical and one based on intuitionistic logic; these systems were conservative extensions of first-order Peano and Heyting arithmetic, respectively. In this paper we study how adding the principle of countable saturation to these systems affects their proof-theoretic strength. We will show that adding countable saturation to our intuitionistic system does not increase its proof-theoretic strength, while adding it to the classical system increases the strength from first- to full second-order arithmetic.
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Eyvind Briseid was supported by the Research Council of Norway (Project 204762/V30), while Pavol Safarik was supported by the German Science Foundation (DFG Project KO 1737/5-1).
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van den Berg, B., Briseid, E. & Safarik, P. The strength of countable saturation. Arch. Math. Logic 56, 699–711 (2017). https://doi.org/10.1007/s00153-017-0567-2
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DOI: https://doi.org/10.1007/s00153-017-0567-2