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The full binary tree cannot be interpreted in a chain

Published online by Cambridge University Press:  12 March 2014

Alexander Rabinovich*
Affiliation:
The Blavatnik School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel. E-mail: [email protected]

Abstract

We show that for no chain C there is a monadic-second order interpretation of the full binary tree in C.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2010

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References

REFERENCES

[Bu62]Büchi, J. R., On a decision method in restricted second order arithmetic, Logic, Methodology and Philosophy of Science, Stanford University Press, 1962, pp. 111.Google Scholar
[BS73]Büchi, J. R. and Siefkes, D., The monadic second order theory of all countable ordinals, Lecture Notes in Mathematics, vol. 328, Springer, 1973.Google Scholar
[ER66]Elgot, C. and Rabin, M. O., Decidability and Undecidability of Extensions of Second (First) Order Theory of (Generalized) Successor, this Journal, vol. 31 (1966), no. 2, pp. 169181.Google Scholar
[FV59]Feferman, S. and Vaught, R. L., The first order properties of products of algebraic systems. Fundamenta Mathematicae, vol. 47 (1959), pp. 57103.CrossRefGoogle Scholar
[GMS83]Gurevich, Y., Magidor, M., and Shelah, S., The monadic theory of ω2, this Journal, vol. 48 (1983), pp. 387398.Google Scholar
[GS89]Gurevich, Y and Shelah, S., On the strength of the interpretation method, this Journal, vol. 54 (1989), pp. 305323.Google Scholar
[LS97]Lifsches, S. and Shelah, S., Peano arithmetic may not be interpretable in the monadic theory of linear orders, this Journal, vol. 62 (1997), pp. 848872.Google Scholar
[LS98]Lifsches, S. and Shelah, S., Uniformization and Skolem functions in the class of trees, this Journal, vol. 63 (1998), pp. 103127.Google Scholar
[LS99]Lifsches, S. and Shelah, S., Random graphs in the monadic theory of order. Archive for Mathematical Logic, vol. 38 (1999), pp. 273312.CrossRefGoogle Scholar
[Rab69]Rabin, M. O., Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp. 135.Google Scholar
[Ro82]Rosenstein, J. G., Linear orderings, Academic Press Inc., New York, 1982.Google Scholar
[Sh75]Shelah, S., The monadic theory of order, Annals of Mathematics. Second Series, vol. 102 (1975), pp. 379419.CrossRefGoogle Scholar