Constraint Satisfaction Problems

When proving theorems, we have a luxury that is so fundamental, we often take it for granted: If we need to work with an object, we say “let x be \(\langle\) the object in question\(\rangle\)” and we move on with the proof. Especially in the finite setting it is obvious that, given enough patience, we should be able to find the object: Simply try out all possibilities and, if there is an object as desired, at least one of them will work. As long as we are not interested in the object itself, this approach is very efficient for developing a theory.