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ordered Kock field
Context
Algebra
- algebra, higher algebra
- universal algebra
- monoid, semigroup, quasigroup
- nonassociative algebra
- associative unital algebra
- commutative algebra
- Lie algebra, Jordan algebra
- Leibniz algebra, pre-Lie algebra
- Poisson algebra, Frobenius algebra
- lattice, frame, quantale
- Boolean ring, Heyting algebra
- commutator, center
- monad, comonad
- distributive law
Group theory
Ring theory
Module theory
Contents
Idea
A definition of ordered field in constructive mathematics which uses denial inequality. It is primarily used in synthetic differential geometry.
Definition
An ordered Kock field is a Kock field with a strict weak order which is not necessarily connected:
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for all ,
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for all and , if , then
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for all , , and , if , then or
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for all and , if and , then
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for all and , if and , then
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for all , if and only if or
See also
References
Last revised on August 19, 2024 at 15:14:57.
See the history of this page for a list of all contributions to it.