B. van den Berg
- The strength of countable saturation
- Archive for Mathematical Logic
- Volume | Issue number
- 56 | 5-6
- Pages (from-to)
- Document type
- Interfacultary Research Institutes
Faculty of Science (FNWI)
- Institute for Logic, Language and Computation (ILLC)
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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