Borel sets with large squares

  title={Borel sets with large squares},
  author={Saharon Shelah},
  journal={arXiv: Logic},
  • S. Shelah
  • Published 1998
  • Mathematics
  • arXiv: Logic
For a cardinal mu we give a sufficient condition (*)_mu (involving ranks measuring existence of independent sets) for: [(**)_mu] if a Borel set B subseteq R x R contains a mu-square (i.e. a set of the form A x A, |A|= mu) then it contains a 2^{aleph_0}-square and even a perfect square, and also for [(***)_mu] if psi in L_{omega_1, omega} has a model of cardinality mu then it has a model of cardinality continuum generated in a nice, absolute way. Assuming MA + 2^{aleph_0}> mu for… Expand
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