Definable linear orders in (Z;<,+) are exactly the (Z;<,+)-definably embeddable ones into lex order on Z^n for some n.
Comptes Rendus du I congr` es de Math´ ematiciens des Pays Slaves , 92–101 (1929) – English translation in [13]
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Linear Orders in Presburger Arithmetic
Definable linear orders in (Z;<,+) are exactly the (Z;<,+)-definably embeddable ones into lex order on Z^n for some n.