The strength of countable saturation
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| Publication date | 08-2017 |
| Journal | Archive for Mathematical Logic |
| Volume | Issue number | 56 | 5-6 |
| Pages (from-to) | 699-711 |
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| 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. |
| Document type | Article |
| Language | English |
| Published at | https://doi.org/10.1007/s00153-017-0567-2 |
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The strength of countable saturation
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