Borel's conjecture in topological groups

@article{Galvin2013BorelsCI,
  title={Borel's conjecture in topological groups},
  author={Fred Galvin and Marion Scheepers},
  journal={J. Symb. Log.},
  year={2013},
  volume={78},
  pages={168-184}
}
We introduce a natural generalization of Borel’s Conjecture. For each infinite cardinal number κ, let BCκ denote this generalization. Then BCא0 is equivalent to the classical Borel conjecture. Assuming the classical Borel conjecture,¬BCא1 is equivalent to the existence of a Kurepa tree of heightא1. Using the connection of BCκ with a generalization of Kurepa’s Hypothesis, we obtain the following consistency results: (1) If it is consistent that there is a 1-inaccessible cardinal then it is… CONTINUE READING

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