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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Arborescent structures. II. Interpretability in the theory of trees


Author: James H. Schmerl
Journal: Trans. Amer. Math. Soc. 266 (1981), 629-643
MSC: Primary 03C65; Secondary 03B15, 03B25, 03C15, 03F25, 06A10
DOI: https://doi.org/10.1090/S0002-9947-1981-0617556-9
MathSciNet review: 617556
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Abstract: The first-order theory of arborescent structures is shown to be completely faithfully interpretable in the first-order theory of trees. It follows from this interpretation that Vaught's conjecture is true for arborescent structures, the theory of arborescent structures is decidable, and every $ {\aleph _0}$-categorical arborescent structure has a decidable theory.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0617556-9
Article copyright: © Copyright 1981 American Mathematical Society