HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES

@article{Fuchs2018HIERARCHIESOF,
  title={HIERARCHIES OF FORCING AXIOMS, THE CONTINUUM HYPOTHESIS AND SQUARE PRINCIPLES},
  author={Gunter Fuchs},
  journal={The Journal of Symbolic Logic},
  year={2018},
  volume={83},
  pages={256 - 282}
}
  • G. Fuchs
  • Published 1 March 2018
  • Economics
  • The Journal of Symbolic Logic
Abstract I analyze the hierarchies of the bounded and the weak bounded forcing axioms, with a focus on their versions for the class of subcomplete forcings, in terms of implications and consistency strengths. For the weak hierarchy, I provide level-by-level equiconsistencies with an appropriate hierarchy of partially remarkable cardinals. I also show that the subcomplete forcing axiom implies Larson’s ordinal reflection principle at ω 2, and that its effect on the failure of weak squares is… 
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  • Economics
    The Journal of Symbolic Logic
  • 2018
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  • G. Fuchs
  • Environmental Science
    J. Math. Log.
  • 2021
For an arbitrary forcing class [Formula: see text], the [Formula: see text]-fragment of Todorčević’s strong reflection principle SRP is isolated in such a way that (1) the forcing axiom for [Formula:
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  • G. Fuchs
  • Environmental Science
    The Journal of Symbolic Logic
  • 2021
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A special case of the main result is that for forcing classes that don’t add reals, the three principles at level $2^\omega $ are equivalent.
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Abstract It is shown that the resurrection axiom and the maximality principle may be consistently combined for various iterable forcing classes. The extent to which resurrection and maximality
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