Nonstandardness and the bounded functional interpretation

نویسندگان

  • Fernando Ferreira
  • Jaime Gaspar
چکیده

The bounded functional interpretation of arithmetic in all finite types is able to interpret principles like weak König’s lemma without the need of any form of bar recursion. This interpretation requires the use of intensional (rule-governed) majorizability relations. This is a somewhat unusual feature. The main purpose of this paper is to show that if the base domain of the natural numbers is extended with nonstandard elements, then the bounded functional interpretation can be seen as falling out from a functional interpretation of nonstandard number theory without intensional notions. The original bounded functional interpretation can be seen as the trace left behind by the new interpretation when one sees it restricted to the standard number theoretical setting. We also answer an open question regarding the conservativity of the transfer principle via-à-vis functional interpretations of nonstandard arithmetic.

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عنوان ژورنال:
  • Ann. Pure Appl. Logic

دوره 166  شماره 

صفحات  -

تاریخ انتشار 2015