A Multidimensional Central Sets Theorem
نویسنده
چکیده
t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in any finite partition of N one of the cells is an IP-set. K. Milliken and A. Taylor ([7, 8]) found a quite natural common extension of the Theorems of Hindman and Ramsey: For a sequence 〈xn〉n=0 in N and k ≥ 1 put [FS(〈xn〉n=0)] k < := nn
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عنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 15 شماره
صفحات -
تاریخ انتشار 2006