Two remarks on set theory
نویسندگان
چکیده
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...
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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...
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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...
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Quasi-set theory is a theory for dealing with collections of indistinguishable objects. In this paper we discuss some logical and philosophical questions involved with such a theory. The analysis of these questions enable us to provide the first grounds of a possible new view of physical reality, founded on an ontology of non-individuals, to which quasi-set theory may constitute the logical basis.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1957
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-10487