 The rise of mathematical logic in the first half of the twentieth century was interwoven with different approaches to understanding the infinite structures of the natural and the real numbers. With the emergence of computer science in the second half of the twentieth century logic went through a process of rebirth. The concepts of a computation and of a database both emphasized the need to understand not so much the finite/infinite distinction as the new measures of degrees of finiteness. For example, the question whether a problem can be decided in polynomial time arose to challenge the well-developed theory of what can be decided in finite time. The analogy between finite relational structures and databases led to the emergence of finite model theory. For a good review we refer to Fagin (1993).