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Interpreting weak Kőnig's lemma in theories of nonstandard arithmetic
Author(s) -
Dinis Bruno,
Ferreira Fernando
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600066
Subject(s) - lemma (botany) , mathematics , arithmetic , pure mathematics , discrete mathematics , poaceae , ecology , biology
We show how to interpret weak Kőnig's lemma in some recently defined theories of nonstandard arithmetic in all finite types. Two types of interpretations are described, with very different verifications. The celebrated conservation result of Friedman's about weak Kőnig's lemma can be proved using these interpretations. We also address some issues concerning the collecting of witnesses in herbrandized functional interpretations.