Theory  Kinds of objects (notions) 
Generic theories  Pure elements classified by types to play different roles 
Set theory  Elements, sets, functions, operations, relations, tuples... 
Model theory  Theories, systems and their components (listed below) 
Onemodel theory  Objects, symbols, types or other notions, Booleans, structures (operators, predicates), expressions (terms, formulas)... 
Arithmetic  Natural numbers 
Linear Algebra  Vectors, scalars... 
Geometry  Points, straight lines, circles... 
By its notion of «object», onemodel theory distinguishes the objects of T in M among its own objects in [T,M], that are the metaobjects. The above rule of use of the meta prefix would let every object be a metaobject; but we will make a vocabulary exception by only calling metaobject those which are not objects: symbols, types or other notions, structures, expressions...
Set theory only knows the ranges of some of its own variables, seen as objects (sets). But, seen by onemodel theory, every variable of a theory has a range among notions, which are metaobjects only.Set theory and Foundations of mathematics  
1. First
foundations of mathematics 1.1. Introduction
to the foundations of mathematics
⇨ 1.4. Structures of mathematical systems1.2. Variables, sets, functions and operations ⇦ 1.3. Form of theories: notions, objects, metaobjects 
1.6. Logical connectives
1.7. Classes in set theory 1.8. Binders in set theory 1.9. Quantifiers 1.10. Formalization of set theory 1.11. Set generation principle 

⇨ Philosophical aspects  Interpretation
of classes Concepts of truth in mathematics 

2. Set theory (continued)  3. Algebra  4. Model theory 