Triangulating non-Archimedean probability

Hazel Brickhill; Leon F M Horsten

doi:10.1017/S1755020318000060

Triangulating non-Archimedean probability

Hazel Brickhill, Leon F M Horsten

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

257 Downloads (Pure)

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.

Original language	English
Pages (from-to)	519-546
Number of pages	27
Journal	Review of Symbolic Logic
Volume	11
Issue number	3
Early online date	24 Jul 2018
DOIs	https://doi.org/10.1017/S1755020318000060
Publication status	Published - 26 Oct 2018

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N2 - 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.

AB - 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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DO - 10.1017/S1755020318000060

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