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TRIANGULATING NON-ARCHIMEDEAN PROBABILITY

  • HAZEL BRICKHILL (a1) and LEON HORSTEN (a2)
Abstract

We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.

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Corresponding author
*GRADUATE SCHOOL OF ENGINEERING KOBE UNIVERSITY 1-1 ROKKODAI-CHO KOBE 657-8501, JAPAN E-mail: brickhill@dragon.kobe-u.ac.jp
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF BRISTOL BRISTOL BS6 6JL, UK E-mail: leon.horsten@bristol.ac.uk
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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
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