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Definably extending partial orders in totally ordered structures
Author(s) -
Ramakrishnan Janak,
Steinhorn Charles
Publication year - 2014
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.201300047
Subject(s) - mathematics , order (exchange) , partially ordered set , combinatorics , pure mathematics , discrete mathematics , economics , finance
We show, for various classes of totally ordered structures M = ( M , < , ... ) , including o‐minimal and weakly o‐minimal structures, that every definable partial order on a subset of M n extends definably in M to a total order. This extends the result proved in [5][D. Macpherson, 1997] for n = 1 and M o‐minimal.