A linearly ordered set is short if it does not contain any monotonic sequence of length \omega₁, and it is long if it contains a monotonic sequence of length \alpha for every ordinal \alpha < (2^\omega)⁺. We prove that there exists a family F of power 2^2\omega of long ordered fields of size 2^\omega that are pairwise nonisomorphic (as fields) and such that every field F in F has 2^2\omega nonisomorphic short subdomains whose field of quotients is F. The generalization of this result for higher cardinals is also discussed. This generalizes the author's result of [Krzysztof Ciesielski, A short ordered commutative domain whose quotient field is not short, Algebra Universalis 25 (1988), 1-6].

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Last modified August 21, 1999.