Countable indecomposable dispersed order types. (English. Russian original) Zbl 0358.06002
Math. Notes 13, 67-70 (1973); translation from Mat. Zametki 13, 113-120 (1973).
Summary: 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, up to equivalence, the finite product of order types of the form \(\omega^k\), \((\omega^k){}^*\), \(\gamma_i\), \(\gamma_i^*\), where \(k\) is arbitrary, and \(i\) is the limiting ordinal.
MSC:
| 06A05 | Total orders |
| 03E20 | Other classical set theory (including functions, relations, and set algebra) |
References:
| [1] | B. Rotman, ?On countable indecomposable order types,? J. London Math. Soc., second series,2, No. 1, 33?39 (1970). · Zbl 0212.02203 · doi:10.1112/jlms/s2-2.1.33 |
| [2] | 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). · Zbl 0111.01201 |
| [3] | R. Laver, ?On Fraisse’s order type conjecture,? Ann. Math.,93, No. 1, 89?111 (1971). · Zbl 0208.28905 · doi:10.2307/1970754 |
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