A linearly ordered set is short if it does not contain any monotonic
sequence of length \omega_{1}, 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.**