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TRIANGULATING NON-ARCHIMEDEAN PROBABILITY

Published online by Cambridge University Press:  24 July 2018

HAZEL BRICKHILL  and
LEON HORSTEN
HAZEL BRICKHILL*
Affiliation:
Graduate School of Engineering, Kobe University
LEON HORSTEN*
Affiliation:
Department of Philosophy, University of Bristol
*
*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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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.

Keywords

03B4226E3028E0560A05nonstandard probabilitynon-Archimedean probabilityPopper functionslexicographic probabilityinfinitesimals
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 3 , September 2018 , pp. 519 - 546
Copyright
Copyright © Association for Symbolic Logic 2018 

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