منابع مشابه
Some Remarks on Set Theory
Let there be given n ordinals cti, alt • • • , an. It is well known that every ordinal can be written uniquely as the sum of indecomposable ordinals. (An ordinal is said to be indecomposable if it is not the sum of two smaller ordinals.) Denote by (ct...
متن کاملSome Remarks on Set Theory
Let there be given n ordinals al, a2, • • • , an . It is well known that every ordinal can be written uniquely as the sum of indecomposable ordinals. (An ordinal is said to be indecomposable if it is not the sum of two smaller ordinals .) Denote by ¢(a) the largest of these indecomposable ordinals belonging to a . (4(a) may have a coefficient c in the decomposition of a.) Put y=minis . 0(ai), a...
متن کاملSome Remarks on Set Theory Iv
This theorem clearly strengthens one part of Sierpinski's result . To prove the theorem, let {la } (a < S2 1 ) be a well-ordering of the lines in the plane, and let 1 1 belong to Li . We begin the construction of the sets S1 and S 2 by assigning all points of 11 to S3-i . Suppose that for (3 < a the points of the lines 1,6 have been divided between S 1 and S 2f and that la belongs to Li . Then ...
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Now, in analogy to Ramsay's theorem, one might consider the following problem. Suppose that, for some u > 0, there is associated with each k-tuple X = {x l , • • • , xk } of elements of an infinite set S a measurable set F(X) of [0, 1] such that m(F(X)) > u . Does there always exist an infinite subset S' of S such that the sets F(X) corresponding to the k-tuples X of S' have a nonempty intersec...
متن کاملSome Remarks on Number Theory
This note contains some disconnected minor remarks on number theory . 1 . Let (1) Iz j I=1, 1<j<co be an infinite sequence of numbers on the unit circle . Put n s(k, n) _ z~, Ak = Jim sup I s(k, n) j=1 k=oo and denote by B k the upper bound of the numbers I s(k,n)j . If z j = e 2nij' a =A 0 then all the Ak 's are finite and if the continued fraction development of a has bounded denominators the...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1953
ISSN: 0026-2285
DOI: 10.1307/mmj/1028989869