منابع مشابه
Some Theorems and Applications of Ramsey Theory
We present here certain theorems in Ramsey theory and some of their applications. First is Ramsey’s Theorem, which concerns the existence of monochromatic complete subgraphs of colored graphs that are large enough. One application is Schur’s Theorem, which is used for a result relating to Fermat’s Last Theorem. We then present the Hales-Jewett Theorem, which can be used to prove van der Waerden...
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New lower bounds for 15 classical Ramsey numbers are established. Several of the colorings are found using a new variation of local search heuristics. Several others are found using known colorings as building blocks. AMS Subject Classifications: 05D10, 05D04
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This paper continues the study of the Ramsey-like large cardinals introduced in [Git09] and [WS08]. Ramsey-like cardinals are defined by generalizing the “existence of elementary embeddings” characterization of Ramsey cardinals. A cardinal κ is Ramsey if and only if every subset of κ can be put into a κ-size transitive model of ZFC for which there exists a weakly amenable countably complete ult...
متن کاملRamsey-like cardinals
One of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. I introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. T...
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Besides using standard radial basis functions, there are a few good reasons to look for kernels with special properties. This survey will provide several examples, starting from an introduction into kernel construction techniques. After providing the “missing” Wendland functions, we focus on kernels based on series expansions. These have some very interesting special cases, namely polynomial an...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1984
ISSN: 0304-3975
DOI: 10.1016/0304-3975(84)90110-5