Homotopy Type Theory
ordered integral domain > history (Rev #4, changes)
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Definition
erm… Anordered integral domain is a totally ordered commutative ring? which comes with a strict order such that
With strict order
- for all elements and , if and , then
- for all elements and , if and , then
- for all elements and , if and , then
An ordered integral domain is a strictly ordered integral -algebra such that for every element such that , there is an element such that .
With positivity
An ordered integral domain is a Heyting integral domain 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
Examples
See also
Revision on June 13, 2022 at 00:52:15 by
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