> some owners are breeders and some breeders are owners
The "Entities" are
* Person (person_id*, name, etc)
* Breeder (breeder_id*, person_id, specialty, etc)
* Owner (owner_id*, person_id, etc)
(* = PRIMARY KEY, probably AUTO_INCREMENT)
Also
* Horse (horse_id*, owner_id, breed, sire, dam, ...) -- Note: this allows one owner to have many horses.
If you also need a horse to have many owners ("many-to-many relationship"), then:
* Horse (horse_id*, breed, sire, dam, ...) -- no owner_id
* HorseOwner (horse_id, owner_id) -- this would have PRIMARY KEY(horse_id, owner_id) (or vice versa) -- This is a "Relationship" table. (It could have extra fields, such as when_purchased, purchase_price, ...
The Syndicate is another "Entity" table. Again, there would be a 1:many or many:many relationship to Owners.
Your queries would have lots of JOINs. Optionally, you could establish "FOREIGN KEYs". You could hide the complexity in VIEWs.
More on the "ER" (Entity-Relationship) modeling:
http://forums.mysql.com/read.php?125,422961 (Simple Database Design Problem)
http://forums.mysql.com/read.php?10,434331 (Circular reference)
http://forums.mysql.com/read.php?125,401536 (Database efficiency question)
http://forums.mysql.com/read.php?10,379859 (school exercise I am suck on)
http://forums.mysql.com/read.php?10,432104 (Design for complex problem)
http://forums.mysql.com/read.php?125,397603 (Help with schema for camera trap tracker)
http://forums.mysql.com/read.php?125,356594 (Database Build - Game concept / inventory management)
http://forums.mysql.com/read.php?125,356144 (Table Structure)
http://forums.mysql.com/read.php?10,241802 (Having trouble designing...)
http://forums.mysql.com/read.php?10,414454 (Database relationship when one entity is optional)
http://forums.mysql.com/read.php?125,261725 (Node/Edge design decision)