Recursive Ramsey Theory
نویسندگان
چکیده
The illustration on the cover is a stylized portrait of Frank Ramsey.
منابع مشابه
Sharp thresholds for the phase transition between primitive recursive and Ackermannian Ramsey numbers
We compute the sharp thresholds on g at which g-large and g-regressive Ramsey numbers cease to be primitive recursive and become Ackermannian. We also identify the threshold below which g-regressive colorings have usual Ramsey numbers, that is, admit homogeneous, rather than just min-homogeneous sets.
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In Ramsey theory, very large numbers and fast-growing functions are more of a rule than an exception. The classical Ramsey numbers R(n,m) are known to be of exponential size: the original proof directly gives the upper bound R(n,m) ≤ ( m+n−2 n−1 ) , and an exponential lower bound is also known. For the van der Waerden numbers, the original proof produced upper bounds that were not even primitiv...
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For a function g : N → N, the g-regressive Ramsey number of k is the least N so that N min −→ (k)g. This symbol means: for every c : [N ] → N that satisfies c(m, n) ≤ g(min{m, n}) there is a min-homogeneous H ⊆ N of size k, that is, the color c(m, n) of a pair {m, n} ⊆ H depends only on min{m, n}. It is known ([4, 5]) that Id-regressive Ramsey numbers grow in k as fast as Ack(k), Ackermann’s fu...
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Stiglitz (Econometrica 37 (1969) 382) shows income convergence in a many-agent Solow growth model with integrated capital markets (ICM). The many-agent Ramsey model (MARM) without ICM also gives income convergence. With a MARM, equal discount rates, and ICM, convergence of incomes (as opposed to product per capita) cannot occur. These results depend upon fixed saving propensities (Stiglitz) or ...
متن کاملPhase Transition Thresholds for Some Natural Subclasses of the Computable Functions
In this paper we first survey recent advances on phase transition phenomena which are related to natural subclasses of the recursive functions. Special emphasis is put on descent recursive functions, witness bounding functions for well-partial orders and Ramsey functions. In the last section we prove in addition some results which show how the asymptotic of the standard Ramsey function is affec...
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تاریخ انتشار 2005