Small cardinals and small Efimov spaces

@article{Brian2022SmallCA,
  title={Small cardinals and small Efimov spaces},
  author={William R. Brian and Alan Dow},
  journal={Ann. Pure Appl. Log.},
  year={2022},
  volume={173},
  pages={103043}
}
  • W. Brian, A. Dow
  • Published 18 January 2019
  • Mathematics
  • Ann. Pure Appl. Log.
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References

SHOWING 1-10 OF 36 REFERENCES
Ultrafilters with small generating sets
It is consistent, relative to ZFC, that the minimum number of subsets ofω generating a non-principal ultrafilter is strictly smaller than the dominating number. In fact, these two numbers can be any
COMPACT SETS WITHOUT CONVERGING SEQUENCES IN THE RANDOM REAL MODEL
It is shown that in the model obtained by adding any number of random reals to a model of CH, there is a compact Hausdor space of weight !1 which contains no non-trivial converging sequences. It is
Accessible and Biaccessible Points in Contrasequential Spaces a
ABSTRACT. Two countable spaces having no nontrivial convergent sequences are constructed. One space has every point biaccessible (by a countable discrete set), and the other has every point
THE COINITIALITY OF A COMPACT SPACE
This article deals with the coinitiality of topological spaces, a concept that generalizes the conality of a Boolean algebra as introduced by Koppelberg (7). The compact spaces of countable
Combinatorial Cardinal Characteristics of the Continuum
The combinatorial study of subsets of the set N of natural numbers and of functions from N to N leads to numerous cardinal numbers, uncountable but no larger than the continuum. For example, how many
EFIMOV SPACES AND THE SPLITTING NUMBER
An Efimov space is a compact space which contains neither a nontrivial converging sequence nor a copy of the Stone-Cech compactification of the integers. We give a new construction of a space which
Efimov's problem
On the Existence of Large p-Ideals
We prove the existence of p -ideals that are nonmeagre subsets of ( ω ) under various set-theoretic assumptions.
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4
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