Sh:1257

• Shelah, S. Homogeneous forcing. Preprint.
• Abstract:
  Assume \kappa = \kappa^{<\kappa} > \aleph_0 (usually \aleph_0 or an inaccessible.)

  We shall deal with iterated forcings preserving {}^{\kappa>}Ord and not collapsing cardinals along a linear order. The aim is to have homogeneous ones, so that for some natural ideals on {}^\kappa2, we get a model of ZF + DC_\kappa\ + “modulo this ideal, every set is equivalent to a \kappa-Borel one."

  The main application is improving the consistency result of Kellner and Shelah [Sh:859], and Horowitz and Shelah [Sh:1067] on saccharinity. But presently, the homogeneity is only forcing ({Q}_t,\mathbf{q} \upharpoonright L_{\mathbf{q},t}).

• Version 2024-11-01 (25p)

@article{Sh:1257,
 author = {Shelah, Saharon},
 title = {{Homogeneous forcing}}
}