If for any complete preference subset of E, there is

denumerable set {[x.sub.n]} [subset] M such that if x [member of] M, x [not equal to] sup M, there is [mathematical expression not reproducible], then E is said to be pseudo separable in incomplete preference.

The problem has a

denumerable set of real eigenvalues (cf.

It is a state space that can be a limited and

denumerable set or a nonempty set.

(1) For any [sigma] > 0, there exist the

denumerable set of positive eigenvalues [[chi].sub.i]([sigma]), where i = 1, 2, ..., of a finite multiplicity with only cumulative point at infinity.

Si'lnikov, "A case of the existence of a

denumerable set of periodic motions," Soviet Mathematics, Doklady, vol.

Given a

denumerable set S and an infinite denumerable class C of overlapping directed circuits (or directed cycles) with distinct points (except for the terminals) in S such that all the points of S can be reached from one another following paths of circuit edges; that is, for each two distinct points i and j of S there exists a finite sequence [c.sub.1], ...

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be the

denumerable set which achieves that maximum [v.sub.1](N([OMEGA])), i,e;

Let G acting on a

denumerable set E and R be a relational structure such that AutR = [bar.G].

To develop this argument, Putnam first introduces the

denumerable set MAG of all knowable physical magnitudes, and then OP, the set of values of the members of MAG at each of denumerably many spacetime points.

It is clear that the model M (the family M) includes absolutely

denumerable sets. We consider the family M as the interpretation of the signature symbol "S " and will show that any axiom of ZFK is either true in the model M or it does not deny the existence of such a model.

The number of elements in one of these

denumerable sets is called the cardinal number, or cardinality.