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Transactions of the American Mathematical Society

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

 

 

Degrees of indiscernibles in decidable models


Authors: H. A. Kierstead and J. B. Remmel
Journal: Trans. Amer. Math. Soc. 289 (1985), 41-57
MSC: Primary 03C57; Secondary 03B25, 03D45
MathSciNet review: 779051
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Abstract: We show that the problem of finding an infinite set of indiscernibles in an arbitrary decidable model of a first order theory is essentially equivalent to the problem of finding an infinite path through a recursive $ \omega $-branching tree. Similarly, we show that the problem of finding an infinite set of indiscernibles in a decidable model of an $ \omega $-categorical theory with decidable atoms is essentially equivalent to finding an infinite path through a recursive binary tree.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0779051-X
Article copyright: © Copyright 1985 American Mathematical Society