منابع مشابه
A Partition Calculus in Set Theory P. Erdös and R. Rado
1 . Introduction . Dedekind's pigeon-hole principle, also known as the box argument or the chest of drawers argument (Schubfachprinzip) can be described, rather vaguely, as follows . If sufficiently many objects are distributed over not too many classes, then at least one class contains many of these objects . In 1930 F. P. Ramsey [12] discovered a remarkable extension of this principle which, ...
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In order to make (19) correct we define X., S(n) (n<(o) a little more caref lly and replace lines 21-31 on Page 504 by the following : Let n < co and s ppose that we have already chosen elements xi c S (ia+a, then choose sets A,A'cA(' ) s ch that A<A' ; if on the other hand a~a+a, then ...
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holds for h < w and v < w1 . We have known this result since 1959 . It has been quoted in lectures on the partition calculus by Erdös and there is mention of the theorem in the literature ([3], [7], [11]) . A propf was given in Milner's thesis [6] . However, we have been asked for details of the proof on several occasions and so it seems desirable to have a reference which is more readily avail...
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In this paper, we develop a system of typed lambda-calculus for the Zermelo-Frænkel set theory, in the framework of classical logic. The first, and the simplest system of typed lambda-calculus is the system of simple types, which uses the intuitionistic propositional calculus, with the only connective →. It is very important, because the well known CurryHoward correspondence between proofs and ...
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We propose a number system that is based on set partitions. This represents the third number system that is based on combinatorial objects, the other two being combinations and permutations. A number system based on set partitions is useful in the hardware enumeration of set partitions, which is significantly faster than software enumeration. Specifically, the restricted growth string (b0b1 . ....
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1956
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1956-10036-0