We will present classical multidimensional transfinite inductive arguments leading under the continnum hypothesis to a strong Luzin set (Todorcevic) and to a c.c.c. partial order whose square is not c.c.c. (Galvin). Both of these constructions are related to some colorings of pairs of countable ordinals which found applications in algebra, analysis and topology (e.g., see Wednesday seminar this week). If time permits, we will discuss what happens after adding one or many Cohen reals.