Abstract
It will be shown that the word problem in semi-groups with cancellation is not solvable. The method depends on reducing the unsolvability of the problem in question to a known unsolvable problem connected with the logical computing machines introduced by Post (Post, [1]) and the author (Turing, [1]). In this we follow Post (Post, [2]) who reduced the problem of Thue to this same unsolvable problem.
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