Plewik, Szymon Ideals of nowhere Ramsey sets are isomorphic. (English) Zbl 0809.04007 J. Symb. Log. 59, No. 2, 662-667 (1994). The author introduces a notion of ideal type, which is a triple of cardinal numbers which can be assigned to a wide class of ideals of sets. The significance of this ideal type is that any two ideals with the same ideal type are isomorphic. In the second section of the paper, this result is applied to show (under suitable set-theoretic hypotheses) that if \(S\) is a family of infinite subsets of \(\omega\), then the ideal of all nowhere Ramsey sets which are contained in \(S\) is isomorphic to the ideal of all nowhere Ramsey sets on \(\omega\). Reviewer: N.H.Williams (Brisbane) Cited in 4 Documents MSC: 03E05 Other combinatorial set theory Keywords:ideal type; nowhere Ramsey sets PDFBibTeX XMLCite \textit{S. Plewik}, J. Symb. Log. 59, No. 2, 662--667 (1994; Zbl 0809.04007) Full Text: DOI References: [1] A new proof that analytic sets are Ramsey 39 pp 163– (1974) · Zbl 0292.02054 [2] A model in which the base-matrix tree can not have cofinal branches 52 pp 651– (1987) [3] Commentationes Mathematicae Unhersitatis Carolinae 31 pp 743– (1990) [4] Fundamenta Mathematicae 110 pp 11– (1980) [5] Borel sets and Ramsey’s theorem 38 pp 193– (1973) [6] Fundamenta Mathematicae 127 pp 127– (1986) [7] Annales Mathematicae Silesianae 14 pp 108– (1986) [8] C. R. Hebdomadaires Seances Académie des Sciences Paris 156 pp 1258– (1914) [9] Fundamenta Mathematicae XXII pp 276– (1934) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.