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Definably extending partial orders in totally ordered structures
Mathematical Logic Quarterly 60 (3):205-210 (2014)
Abstract
We show, for various classes of totally ordered structures, including o‐minimal and weakly o‐minimal structures, that every definable partial order on a subset of extends definably in to a total order. This extends the result proved in for and o‐minimal.Other Versions
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Citations of this work
Does weak quasi-o-minimality behave better than weak o-minimality?Slavko Moconja & Predrag Tanović - 2021 - Archive for Mathematical Logic 61 (1):81-103.
References found in this work
Quasi-o-minimal structures.Oleg Belegradek, Ya'acov Peterzil & Frank Wagner - 2000 - Journal of Symbolic Logic 65 (3):1115-1132.
On linearly ordered structures of finite rank.Alf Onshuus & Charles Steinhorn - 2009 - Journal of Mathematical Logic 9 (2):201-239.
The independence of the prime ideal theorem from the order-extension principle.U. Felgner & J. K. Truss - 1999 - Journal of Symbolic Logic 64 (1):199-215.
Extending Partial Orders on o‐Minimal Structures to Definable Total Orders.Dugald Macpherson & Charles Steinhorn - 1997 - Mathematical Logic Quarterly 43 (4):456-464.
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