On the density of families of sets
TLDR
This paper will answer the question in the affirmative by determining the exact upper bound of T if T is a family of subsets of some infinite set S then either there exists to each number n a set A ⊂ S with |A| = n such that |T ∩ A| = 2n or there exists some number N such that •A| c for each A⩾ N and some constant c.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1972-07-01 and is currently open access. It has received 1029 citations till now. The article focuses on the topics: Family of sets & Infinite set.read more
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A combinatorial problem; stability and order for models and theories in infinitary languages.
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Stability, the f.c.p., and superstability; model theoretic properties of formulas in first order theory
Saharon Shelah,Saharon Shelah +1 more
TL;DR: In this paper, the authors investigated in detail stable formulas, ranks of types and their definability, the fcp, some syntactical properties of unstable formulas, indiscernible sets and degrees of types in superstable theories.