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The results in this paper are contained in the Ph. D. thesis [4] of the second author, written under the direction of the first author.
Professor Büchi died suddenly in April 1984 while this paper was still in preparation. He will be greatly missed.
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Büchi, J.R., Senger, S. Coding in the existential theory of concatenation. Arch math Logik 26, 101–106 (1987). https://doi.org/10.1007/BF02017493
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DOI: https://doi.org/10.1007/BF02017493