I want to enumerate given finite class of abstract objects.

What is the class?

1. collection of objects sharing common property

What does it mean to "enumerate" something?

1. to know the first enumerated element
2. to have the algorithm for finding next enumerated element after any enumerated element.
3. The algorithm should always stop for any enumerated element. There should be some proof of that.

What is the object in terms of finite discrete world?

1. it is the composition of parts or an atomic part
2. and there is no such composition which part is the object itself. So object is kind of 'root' part.
3. part itself is the composition of parts or an atomic part
4. There is finite alphabet of atomic parts
5. There is finite number of predicates representing relations between parts.

How to define class of objects?

Object is considered belonging to the specific class iff there is some model of some theory (built over known set of predicates) for which formula IsObject(o) is true.

Enough for today