for the orders, most of them want to share the 14 names that were generated.

the problem is how daamath will present them.

| type | meet | join | 
| - | - | - |
| set | intersection | union |
| boolean | and | or |
| logic | conjunction | disjunction |
| standard order | minimum | maximum |
| divisibility | gcd | lcm |

variadic versions of meet and join behave nicely on lattices, but not so much on general posets

sup/inf (a.k.a glb/lub) shall *not* be defined. these are more general concepts.
