User:Dfeuer/sandbox

Order Completion
Note: I'm guessing these are true, and will attempt to prove them, but I do not yet know that either of them is.
 * User:Dfeuer/Order Completion is Minimal
 * User:Dfeuer/Minimal Enclosing Complete Lattice is Order Completion

Reflexive Closure and Reflexive Reduction

 * Reflexive Reduction of Antisymmetric Relation is Asymmetric

Properties of Compatible Relations

 * User:Dfeuer/Operating on Transitive Relationships Compatible with Operation
 * User:Dfeuer/Compatible Transitive Relation Relates Powers of Related Elements


 * User:Dfeuer/CRG1
 * User:Dfeuer/CRG2
 * User:Dfeuer/CRG3
 * User:Dfeuer/CRG4
 * User:Dfeuer/CTR5

Properties of Ordered Groups

 * User:Dfeuer/Properties of Ordered Group
 * User:Dfeuer/OG1
 * User:Dfeuer/OG2
 * User:Dfeuer/OG3
 * User:Dfeuer/OG4
 * User:Dfeuer/Operating on Ordered Group Relationships
 * User:Dfeuer/OG5


 * User:Dfeuer/Totally Ordered Group with Order Topology is Topological Group

Musings on possible generalizations of or alternate approaches to ordered rings
User:Dfeuer/OR-musings

Properties of Ordered Rings

 * Product of Positive Element and Element Greater than One
 * User:Dfeuer/Strictly Positive Power of Element Greater than One Not Less than Element
 * User:Dfeuer/OR1
 * User:Dfeuer/OR2
 * User:Dfeuer/OR3
 * User:Dfeuer/OR4
 * User:Dfeuer/OR5
 * User:Dfeuer/OR6
 * User:Dfeuer/OR7
 * User:Dfeuer/OR8
 * User:Dfeuer/OR9
 * User:Dfeuer/OR10
 * User:Dfeuer/OR11

Lexicographic Orderings

 * User:Dfeuer/Definition:Lexicographic Ordering on Product
 * User:Dfeuer/Definition:Lexicographic Ordering of Finite Sequences

Useful links
Axiom of Foundation at NLab