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A relation from one set to another, represented by a subset of their Cartesian product.
Order, equivalence, accessibility, and well-foundedness use the endorelation specialization .
wp-relationgierz-orderEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Choose a target set and a subset . Endorelations are the specialization .
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
mathlib-relationsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
First specialize to an endorelation ; restrict to equivalence relations.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-equivalencegierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
Specialize to a relation that is total and single-valued in ; this is exactly a function .
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-functionnlab-functionopenlogic-set-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Specialize to an endorelation on worlds, treat it as accessibility, and assign atomic propositions to worlds.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-kripke-semanticsopenlogic-model-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
First specialize to an endorelation ; restrict to reflexive and transitive relations.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-preordergierz-orderThis is an authored directed relation from the source endpoint to the target endpoint.
First specialize to an endorelation ; require every nonempty subset to have a minimal element.
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
wp-well-foundednlab-well-foundedopenlogic-set-theory