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Definition
Let be an ordered integral domain, and let be the injection of the positive integers into . is an Archimedean ordered integral domain if there is a family of dependent terms
With strict order
is an Archimedean ordered integral domain if there is a family of dependent terms
With positivity
is an Archimedean ordered integral domain if there is a family of dependent terms
Examples
The integers are an Archimedean ordered integral domain.