The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.

this paper) and independently of the matter of considering Church's and Turing's thesis as de nitions (in any philosophical sense), or as empirical or mathematics thesis, we think that Church's thesis and Turing's thesis should have associated a true-value. This true-value is not known, and although is not possible a positive test, we thought that if should be possible a negative one