English

Intuitionistic nonstandard bounded modified realisability and functional interpretation

Logic 2017-12-14 v2

Abstract

We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and Gaspar's functional interpretation and has similarities with Van den Berg, Briseid and Safarik's functional interpretation but replacing finiteness by majorisability. We give a threefold contribution: constructive content and proof-theoretical properties of nonstandard arithmetic; filling a gap in the literature; being in line with nonstandard methods to analyse compactness arguments.

Keywords

Cite

@article{arxiv.1512.07113,
  title  = {Intuitionistic nonstandard bounded modified realisability and functional interpretation},
  author = {Bruno Dinis and Jaime Gaspar},
  journal= {arXiv preprint arXiv:1512.07113},
  year   = {2017}
}

Comments

25 pages

R2 v1 2026-06-22T12:15:55.845Z