Homotopy Type Theory
ordered field > history (Rev #3)
Definition
With strict order
An ordered field is a strictly ordered integral -algebra such that for every element such that , there is an element such that .
With positivity
An ordered field is a commutative ring with a predicate such that
- for every term , if is not positive and is not positive, then
- for every term , if is positive, then is not positive.
- for every term , , if is positive, then either is positive or is positive.
- for every term , , if is positive and is positive, then is positive
- for every term , , if is positive and is positive, then is positive
- for every term , if is positive, then there exists a such that and
Examples
See also
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