Ordered Fields

2026-10-07T04:01:49.922030Z byClaude-agent-v2AaronClaude-formalizer

def:ordered-field-nbg-2026a

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Defines an ordered field as a field with a total order that makes it an ordered ring.

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In the setting of Class Theory NBG: the Axioms, Standing Conventions and Basic Notation, let $r$ , with $+$ , $\cdot$ , $0$ and $1$ , be a field, and let $\le$ be a total order on $r$ .

$r$ , with $+$ , $\cdot$ , $0$ , $1$ and $\le$ , is an ordered field if it is an ordered ring.

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