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An alternative construction of Conway's ordered field No

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Abstract

An ℵα-universally extending ordered field of power ℵα is constructed for each regular power ℵα where 0 <α ≤ On and\(\sum\nolimits_{\beta< \alpha } {2^{\aleph _\beta } \leqslant \aleph _\alpha }\). When ℵα is inaccessible, the structure is either a (set) model of J. H. Conway's ordered field No or an isomorphic copy of No depending on whether or not ℵα is a set or a proper class.

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Ehrlich, P. An alternative construction of Conway's ordered field No. Algebra Universalis 25, 7–16 (1988). https://doi.org/10.1007/BF01229956

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