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Archive for Mathematical Logic

, Volume 56, Issue 5–6, pp 699–711 | Cite as

The strength of countable saturation

  • Benno van den BergEmail author
  • Eyvind Briseid
  • Pavol Safarik
Open Access
Article
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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.

Keywords

Proof theory Nonstandard analysis Arithmetic in all finite types Saturation principles 

Mathematics Subject Classification

03F10 03F25 03F50 11U10 26E35 

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Copyright information

© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute for Logic, Language and ComputationUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.GFU/LUIOslo and Akershus University College of Applied SciencesOsloNorway
  3. 3.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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