Titlebook: Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory; Mauro Di Nasso,Isaac Goldbring,Martino Lupini Book 2019 Springer Nat

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From Hindman to Gowerse most famous early result in this area, several other additive configurations were later shown to be partition regular. Among these there are sets of finite sums of a finite sequence, which is the content of Folkman’s theorem.

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Book 2019will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas..

falsehood

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Hyperfinite Generators of Ultrafiltersin this way. Such an observation makes precise the assertion that ultrafilter proofs can be seen and formulated as nonstandard arguments. The converse is often true but not always, as two different points in a nonstandard extension can give rise to the same ultrafilter.

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Working in the Remote Realmied to characteristic functions of nonstandard extensions. Deviating from Jin’s original formulation, we present his technique using the more recent notion of finite embeddability of subsets of natural numbers due to Di Nasso.

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The Interval Measure Property projection onto the standard unit interval. This leads to a notion of standard subsets of the natural numbers having the Standard Interval Measure Property and we enumerate some basic facts concerning sets with this property.

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0075-8434 Ramsey theory.Provides a self-contained introduction to the .The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent de