A note on equality in finite‐type arithmetic

descriptionPublicationkeyboard_double_arrow_right Article 27 Oct 2017 Netherlands English Publisher:WileyJournal:Mathematical Logic Quarterly, volume 63, pages 282-288 (issn: 0942-5616, eissn: 1521-3870,

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Authors: van den Berg, B.;

doi: 10.1002/malq.201600080

handle: 11245.1/b703fdd8-ba07-4463-92b0-57b8faacb219

A note on equality in finite‐type arithmetic

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Abstract

AbstractWe present a version of arithmetic in all finite types based on a systematic use of an internally definable notion of observational equivalence for dealing with equalities at higher types. For this system both intensional and extensional models are possible, the deduction theorem holds and the soundness of the Dialectica interpretation is provable inside the system itself.

Country

Netherlands

Related Organizations

University of Amsterdam
Netherlands

Keywords

Type theory, Second- and higher-order arithmetic and fragments, 004

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