Journal ArticleDOI
Every analytic set is ramsey
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This article is published in Journal of Symbolic Logic.The article was published on 1970-03-01. It has received 156 citations till now. The article focuses on the topics: Ramsey theory & Analytic set.read more
Citations
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Book ChapterDOI
Combinatorial Cardinal Characteristics of the Continuum
TL;DR: The main results about these cardinal characteristics of the continuum are of two sorts: inequalities involving two (or sometimes three) characteristics, and independence results that other such inequalities cannot be proved in ZFC as discussed by the authors.
Journal ArticleDOI
Internal cohen extensions
Journal ArticleDOI
A new proof that analytic sets are Ramsey
TL;DR: A direct mathematical proof of the Mathias-Silver theorem that every analytic set is Ramsey is given.
Book ChapterDOI
Special Subsets of the Real Line
TL;DR: In this article, a set of reals X of cardinality ω 1 has universal measure zero if for all measures μ on the Borel sets, there is a Borel set of μ-measure zero covering X.
Journal ArticleDOI
Ramsey's theorem with sums or unions
TL;DR: Use Hindman's theorem as a strong pigeonhole principle to prove strengthened versions of Ramsey's theorem and of various generalizations of Ramsey’s theorem due to Nash-Williams, Galvin and Prikry, and Silver.
References
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Journal ArticleDOI
The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis
TL;DR: Godel as discussed by the authors proved the incompleteness theorem of the Continuum Hypothesis, which states that there is no set of numbers between the integers and real numbers, which was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems.
Book
The Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory
TL;DR: Kurt Godel, mathematician and logician, was one of the most influential thinkers of the twentieth century and ranked higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk.
Journal ArticleDOI
Iterated Cohen extensions and Souslin's problem*
Robert Solovay,S. Tennenbaum +1 more
TL;DR: In this article, the real line up to order isomorphism is characterized by the following properties: R is order complete, order dense, has no first or last elements, and contains a countable dense subset.