Abstract
In this paper we consider some properties of indecomposable dispersed order types and estimate the cardinality of the set of distinct indecomposable order types of given rank which can be represented in the form of the product of order types which are not unity. In addition, we refute Rotman's proposition that every countable indecomposable dispersed order type is, to within equivalence, the finite product of order types of the form ωk, (ωk)*, γi, γ *i , where k is arbitrary, and i is the limiting ordinal.
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B. Rotman, “On countable indecomposable order types,” J. London Math. Soc., second series,2, No. 1, 33–39 (1970).
P. Erdös and A. Hajnal, “On a classification of denumerable order types and an application to the partition calculus,” Fund. Math.,51, 117–129 (1962).
R. Laver, “On Fraisse's order type conjecture,” Ann. Math.,93, No. 1, 89–111 (1971).
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Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 113–120, January, 1973.
In conclusion the author wishes to take this opportunity to thank Yu. L. Ershov for his attention to this paper.
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Pinus, A.G. Countable indecomposable dispersed order types. Mathematical Notes of the Academy of Sciences of the USSR 13, 67–70 (1973). https://doi.org/10.1007/BF01093633
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DOI: https://doi.org/10.1007/BF01093633