Morel, Anne C. On the arithmetic of order types. (English) Zbl 0178.31705 Trans. Am. Math. Soc. 92, 48-71 (1959). Reviewer: E. C. Milner Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 Documents MSC: 03Exx Set theory Keywords:set theory × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Anne C. Davis, Cancellation theorems for products of order types I, Bull. Amer. Math. Soc. Abstract 58-1-77. [2] -, On order types whose squares are equal, Bull. Amer. Math. Soc. Abstract 58-3-276. [3] -, Cancellation theorems for products of order types II, Bull. Amer. Math. Soc. Abstract 58-4-330. [4] Anne C. Davis, Sur l’équation \?\(^{n}\)=\? pour des types d’ordre, C. R. Acad. Sci. Paris 235 (1952), 924 – 926 (French). · Zbl 0048.28303 [5] -, Square roots of some denumerable order types, Bull. Amer. Math. Soc. Abstract 59-1-110. [6] Anne C. Davis and W. Sierpiński, Sur les types d’ordre distincts dont les carrés sont égaux, C. R. Acad. Sci. Paris vol. 226 (1952) pp. 850-852. · Zbl 0047.05701 [7] Roland Fraïssé, Sur la comparaison des types d’ordres, C. R. Acad. Sci. Paris 226 (1948), 1330 – 1331 (French). · Zbl 0034.17604 [8] Seymour Ginsburg, Some remarks on order types and decompositions of sets, Trans. Amer. Math. Soc. 74 (1953), 514 – 535. · Zbl 0052.28401 [9] Seymour Ginsburg, Fixed points of products and ordered sums of simply ordered sets, Proc. Amer. Math. Soc. 5 (1954), 554 – 565. · Zbl 0057.04301 [10] Felix Hausdorff, Grundzüge der Mengenlehre, Chelsea Publishing Company, New York, N. Y., 1949 (German). · Zbl 0041.02002 [11] A. Lindenbaum and A. Tarski, Communication sur les recherches de la théorie des ensembles, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, vol. 19 (1926) Classe 3, pp. 299-330. · JFM 57.1330.02 [12] W. Sierpiński, Leçons sur les nombres transfinis, Paris, Gauthier-Villars, 1928. · JFM 54.0087.01 [13] Wacław Sierpiński, Sur la division des types ordinaux, Fund. Math. 35 (1948), 1 – 12 (French). · Zbl 0032.05201 [14] Th. Skolem, Logisch-Kombinatorische Untersuchungen über die Erfüllbarkeit oder Beweisbarkeit mathematischer Sätze nebst einem Theoreme über dichte Mengen, Skrifter utget av Videnskapsselskapet i Kristiania, I klasse, 1920, no. 4. · JFM 48.1121.01 [15] Alfred Tarski, Ordinal algebras, North-Holland Publishing Co., Amsterdam, 1956. With appendices by Chen-Chung Chang and Bjarni Jónsson. · Zbl 0072.00201 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.