A dichotomy for P-ideals of countable sets

@article{Todorcevic2000ADF,
  title={A dichotomy for P-ideals of countable sets},
  author={Stevo Todorcevic},
  journal={Fundamenta Mathematicae},
  year={2000},
  volume={166},
  pages={251-267}
}

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References

SHOWING 1-8 OF 8 REFERENCES

Making the supercompactness of κ indestructible under κ-directed closed forcing

A model is found in which there is a supercompact cardinal κ which remains supercompact in any κ-directed closed forcing extension.

Partitioning pairs of countable ordinals

On montre que les paires d'ordinaux denombrables peuvent etre colorees avec une infinite non denombrable de couleurs de telle sorte que tout ensemble non denombrable contienne des paires de chaque