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Reverse Mathematics and Ordinal Multiplication
Author(s) -
Hirst Jeffry L.
Publication year - 1998
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19980440404
Subject(s) - multiplication (music) , mathematics , countable set , division (mathematics) , reverse mathematics , arithmetic , ordinal data , second order arithmetic , discrete mathematics , algebra over a field , pure mathematics , combinatorics , statistics , axiom , peano axioms , geometry
This paper uses the framework of reverse mathematics to analyze the proof theoretic content of several statements concerning multiplication of countable well‐orderings. In particular, a division algorithm for ordinal arithmetic is shown to be equivalent to the subsystem ATR 0 .
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