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

3 Citations (Scopus)

222 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

Access to Document

10.1017/S1755020318000060Licence: Unspecified

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://doi.org/10.1017/S1755020318000060 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 394 KBLicence: Unspecified

http://arxiv.org/abs/1608.02850Licence: Unspecified

Cite this

@article{8e050ab4801a4f86ade563bec2eb853e,

title = "Triangulating non-Archimedean probability",

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.",

author = "Hazel Brickhill and Horsten, {Leon F M}",

year = "2018",

month = oct,

day = "26",

doi = "10.1017/S1755020318000060",

language = "English",

volume = "11",

pages = "519--546",

journal = "Review of Symbolic Logic",

issn = "1755-0203",

publisher = "Cambridge University Press",

number = "3",

}

TY - JOUR

T1 - Triangulating non-Archimedean probability

AU - Brickhill, Hazel

AU - Horsten, Leon F M

PY - 2018/10/26

Y1 - 2018/10/26

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.

U2 - 10.1017/S1755020318000060

DO - 10.1017/S1755020318000060

M3 - Article (Academic Journal)

VL - 11

SP - 519

EP - 546

JO - Review of Symbolic Logic

JF - Review of Symbolic Logic

SN - 1755-0203

IS - 3

ER -

Triangulating non-Archimedean probability

Abstract

Access to Document

Fingerprint

Cite this