# cofinal

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## cofinal

[kō′fīn·əl]
(mathematics)
A subset C of a directed set D is cofinal if for each element of D there is a larger element in C.
References in periodicals archive ?
Step 2: We extract a strictly well-ordered increasing and cofinal sequence from C.
The second possibility implies that there exists a sequence (sa)aN in S such that v(x- sa) is cofinal in vK.
Fitch assigned bonds of Ryazan Region rating "B+C[yen]; bonds ofLipetsk Region the final rating "BBC[yen]; bonds of Krayinvestbank Cofinal rating "B+C[yen]; upgraded the ratings of Hakasia Republicto "BBC[yen], forecast Co "stableC[yen]; confirmed the rating of Novosibirsk Region; assigned the final rating "BBBCEC[yen] to ruble bonds of Alfa bank.
In this case, ([less than or equal to]) is called a Zorn order when max(X,[less than or equal to]) is nonempty and cofinal in X [for each u [member of] X there exists a ([less than or equal to])-maximal [upsilon] [member of] X with u [less than or equal to] v].
Otra alternativa surgiria de la que sube hacia el puerto de San Isidro, remontando la cuenca del Porma, bifurcandose hacia el Norte tras pasar Cofinal (Rabanal, 1988: 34-35).
Leon: Cofinal, pinar de Lillo, 30TUN1469, 1270 m, 6-VIII-2003, A.
The Generic Orientation finds its mathematical expression in Cohen's work on the continuum problem, which proceeds to show that if we admit certain carefully delineated 'indiscernible' or 'generic' sets into a model for set theory, we produce new models in which the power of the continuum exceeds that of the natural numbers by 'as much as one likes, so that the power set of [[omega].sub.n] may be assigned any cardinality at all that is greater than [[omega].sub.0] (with the single exception that the cardinal selected not be cofinal with [[omega].sub.0]; that is, it cannot be [omega][[omega].sub.0]).
Then [[bar.[epsilon]'(X) = {[bar.E] | E [member of] [epsilon](X), [bar.E] [subset] [bar.[E.sub.0]]} is cofinal and we have [bar.L](X) = [[union].sub.[bar.E][member of][[bar.[epsilon]'(X)] [bar.E] and [??](X) = lim[bar.E][member of][[bar.[epsilon]'(X)] c([bar.E]).
Cofinal, pinar de Lillo, 30TUN1469,1270 m, 6-VIII-2003, A.
The functors [[PI]'.sub.n], [[PI]'.sub.n], [[PI]".sub.n] are left cofinal.
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