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CiE 2019 is the 15th conference organized by CiE (Computability in Europe), a European association of mathematicians, logicians, computer scientists, philosophers, physicists and others interested in new developments in computability and their underlying significance for the real world. The CiE conferences serve as an interdisciplinary forum for research in all aspects of computability, foundations of computer science, logic, and theoretical computer science, as well as the interplay of these areas with practical issues in computer science and with other disciplines such as biology, mathematics, philosophy, or physics.