Assume that [beta] is an

ordinal limit; that is, there exists a strictly ascending sequence [([[beta].sub.n]).sub.n] of

ordinals in [OMEGA] such that [beta] = sup{[[beta].sub.n]; n [member of] N} and [[beta].sub.m] [??] [[beta].sub.n] < [beta] whenever m [less than or equal to] n.

Sin embargo, en cada una de las tres secciones que siguen ofrecemos un argumento contra el Computacionalismo basado en una capacidad concreta: la de generar

ordinales (primer argumento) o la de definir

ordinales (segundo y tercer argumentos).

Ignoring letter width, swap any of the 44 cardinal (first 43

ordinal) sevens above with threes or eights, producing [3.sup.44] cardinals ([3.sup.43]

ordinals) of 758 (760) letters: 3 combinations per 44 (43) independent slots.

Ordinals 12-14 list closely spaced ages of 438, 433, and 464.

Within this group of works the author uses "canon perpetuus" from Sex carmina alcaei as a vehicle for introducing his choice to use fixed-do integers for labelling rows and Andrew Mead's 0-e convention for numbering the

ordinals in a row (pp.

Further on, Field proves a lot of theorems about fixed points and limit

ordinals, i.e.

We are now in a position to consider the construction of the finite

ordinals. The void, or empty set [empty set] can be considered as the first natural

ordinal o, with its singleton {[empty set]} corresponding to the

ordinal i.

Linguistic markers help distinguish cardinals from

ordinals by the use of the -th suffix and different words for first, second, and third, but usually the nominal form is the same as its cardinal form.

The quite modest amount of mathematics required to understand stability semantics (a little bit of set theory, primarily

ordinal arithmetic) is nicely presented; and the various alternatives available for those who favour systems of stability semantics are laid out in a way that makes technical comparisons among them easy.

Now consider Konig's Paradox as an example: there are indefinable

ordinals, and the least indefinable

ordinal has just been defined in that very phrase.

Ordinal data often occur during sampling survey and experimental design; therefore, it is difficult to get the interval data.

In the context of a Burgean semantics, which describes how context supplies

ordinal subscripts to occurrences of "true", one wants to know more than just when an utterance is [true.sub.0] or [true.sub.1] or [true.sub.2].