German for the Decision Problem. This is a question that arose in David Hilbert's dream of building a formal axiomatic system that would encompass all of mathematics. It is the problem of deciding whether a given assertion is a theorem or not, within the bounds of the axiomatic system. However, Kurt Gödel and Alan Turing between themselves showed that for any mathematical system capable of encompassing the whole of arithmetic, there will exist an a unsolvable Entscheidungsproblem, i.e. an assertion can be constructed whose truth or falsity cannot be decided within the mathematical system, that undecidable statements exist.

Log in or registerto write something here or to contact authors.