منابع مشابه
A Partition Theorem
We prove a partition theorem (in the sense of the theorems of Ramsey [3], Erdös-Rado [1], and Rado [2]) which together with a forthcoming paper by Halpern and A. Levy will constitute a proof of the independence of the axiom of choice from the Boolean prime ideal theorem in Zermelo-Fraenkel set theory with the axiom of regularity. Although the theorem arises in logic, it is of a purely combinato...
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We deal with some relatives of the Hales Jewett theorem with primitive recursive bounds.
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We prove a Hindman-type partition theorem for Baire partitions of [0, 1].
متن کاملEuler's Partition Theorem
Euler’s Partition Theorem states that the number of partitions with only distinct parts is equal to the number of partitions with only odd parts. The combinatorial proof follows John Harrison’s pre-existing HOL Light formalization [1]. To understand the rough idea of the proof, I read the lecture notes of the MIT course 18.312 on Algebraic Combinatorics [2] by Gregg Musiker. This theorem is the...
متن کاملA proof of Shelah's partition theorem
<cfμ means: for every coloring c of μ × μ by less than cfμ many colors there are A ⊆ μ with otpA = μ + 1 and B ⊆ μ with otpB = μ such that c is constant on A×B. The proof here is re-arranged slightly differently than the proof in the forthcoming [Sh 513] so that no use of other results of Shelah is made, except for Fact 2 below, which comes from pcf theory. In other words, we avoid here using t...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1966
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1966-0200172-2