WEEK 3
M: An application of recursiion on \omega: R-transitive closures. Recursion along a well-founded relation.
     1.24. Definition. R-transitive closure.
     1.25. Proposition. Existence of R-transitive closures. 
     1.26. Theorem.  Recursion on V along a well-founded relation. 
W: Completion of the proof of Theorem 1.26. A variant of Thm 1.26.
     1.27. Proposition. A set-like relation R is well-founded iff every nonempty class has an R-minimal element.
     1.28. Theorem. Recursion on V along a well-founded relation that allows to assign values to minimal elements.
F: Induction. Isomorphisms. Well-orderings.
     1.29. Theorem. If R is a well-founded set-like relation and A is a class such that
                                   pred_R(x) is a subset of A   ==>    x  is an element of A  
                              for all x then A = V. 
     1.30. Definition. Well-ordering: A linear ordering that is well-founded. 
              Remark. An alternative definition of well-ordering.
     1.31. Definition. Isomorphism of two relational structures.
     1.32. Definition. An R-initial segment of A under a partial ordering A.
     1.33. Proposition. Let (A,R) and (B,S) be two set-like well orderings. Then one of them is isomorphis to
                                    an initial segment of the other.