On the existence of real-closed fields that are 𝜂_{𝛼}-sets of power ℵ_{𝛼}

On the existence of real-closed fields that are $\eta _{\alpha }$-sets of power $\aleph _{\alpha }$
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Trans. Amer. Math. Soc. 103 (1962), 341-352

DOI: https://doi.org/10.1090/S0002-9947-1962-0146089-X

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References

Norman L. Alling, On ordered divisible groups, Trans. Amer. Math. Soc. 94 (1960), 498–514. MR 140595, DOI 10.1090/S0002-9947-1960-0140595-8
Norman L. Alling, A characterization of Abelian $\eta _{\alpha }$-groups in terms of their natural valuation, Proc. Nat. Acad. Sci. U.S.A. 47 (1961), 711–713. MR 175983, DOI 10.1073/pnas.47.5.711

Algebraische Konstruktion reeler Körper

5

Über nicht-Archimedisch geordnete Körper

8

A. H. Clifford, Completion of semi-continuous ordered commutative semigroups, Duke Math. J. 26 (1959), 41–59. MR 101276
Paul F. Conrad, Embedding theorems for abelian groups with valuations, Amer. J. Math. 75 (1953), 1–29. MR 53933, DOI 10.2307/2372611
Paul Conrad, On ordered division rings, Proc. Amer. Math. Soc. 5 (1954), 323–328. MR 61582, DOI 10.1090/S0002-9939-1954-0061582-7
P. Erdös, L. Gillman, and M. Henriksen, An isomorphism theorem for real-closed fields, Ann. of Math. (2) 61 (1955), 542–554. MR 69161, DOI 10.2307/1969812
Isidore Fleischer, Maximality and ultracompleteness in normed modules, Proc. Amer. Math. Soc. 9 (1958), 151–157. MR 93693, DOI 10.1090/S0002-9939-1958-0093693-8
L. Gillman, Some remarks on $\eta _\alpha$-sets, Fund. Math. 43 (1956), 77–82. MR 79069, DOI 10.4064/fm-43-1-77-82
Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
K. A. H. Gravett, Valued linear spaces, Quart. J. Math. Oxford Ser. (2) 6 (1955), 309–315. MR 87649, DOI 10.1093/qmath/6.1.309
K. A. H. Gravett, Ordered abelian groups, Quart. J. Math. Oxford Ser. (2) 7 (1956), 57–63. MR 91955, DOI 10.1093/qmath/7.1.57

Über die nichtarchimedischen Grössensysteme

116

Felix Hausdorff, Felix Hausdorff—gesammelte Werke. Band II, Springer-Verlag, Berlin, 2002 (German). “Grundzüge der Mengenlehre”. [“Foundations of set theory”]; Edited and with commentary by E. Brieskorn, S. D. Chatterji, M. Epple, U. Felgner, H. Herrlich, M. Hušek, V. Kanovei, P. Koepke, G. Preuß, W. Purkert and E. Scholz. MR 2229142
Irving Kaplansky, Maximal fields with valuations, Duke Math. J. 9 (1942), 303–321. MR 6161

Allgemeine Bewertungstheorie

167

Saunders MacLane, The universality of formal power series fields, Bull. Amer. Math. Soc. 45 (1939), 888–890. MR 610, DOI 10.1090/S0002-9904-1939-07110-3
B. H. Neumann, On ordered division rings, Trans. Amer. Math. Soc. 66 (1949), 202–252. MR 32593, DOI 10.1090/S0002-9947-1949-0032593-5
Alexander Ostrowski, Untersuchungen zur arthmetischen Theorie der Körper, Math. Z. 39 (1935), no. 1, 269–320 (German). MR 1545505, DOI 10.1007/BF01201361

Sur une propriété des ensembles ordonnés

36

Sur les classes d’ensembles closes par rapport à certaines opérations élémentaires

16

Daniel Zelinsky, Nonassociative valuations, Bull. Amer. Math. Soc. 54 (1948), 175–183. MR 23815, DOI 10.1090/S0002-9904-1948-08980-7