Directed sets and cofinal types

@article{Todorcevic1985DirectedSA,
  title={Directed sets and cofinal types},
  author={Stevo Todorcevic},
  journal={Transactions of the American Mathematical Society},
  year={1985},
  volume={290},
  pages={711-723}
}
  • S. Todorcevic
  • Published 1 February 1985
  • Mathematics
  • Transactions of the American Mathematical Society
We show that 1, S. @1, X x xl and [l]<@ are the only cofinal types of directed sets of size Sl, but that there exist many cofinal types of directed sets of size continuum. A partially ordered set D is directed if every two elements of D have an upper bound in D. In this note we consider some basic problems concerning directed sets which have their origin in the theory of Moore-Smith convergence in topology [12, 3, 19, 9]. One such problem is to determine "all essential kind of directed sets… 
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