The strength of countable saturation

作者：van den Berg Benno^*; Briseid Eyvind; Safarik Pavol

来源：Archive for Mathematical Logic, 2017, 56(5-6): 699-711.

DOI：10.1007/s00153-017-0567-2

• Proof theory
• Nonstandard analysis
• Arithmetic in all finite types
• Saturation principles

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.

• 出版日期2017-8