HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS

@article{Fuchs2018HIERARCHIESO,
  title={HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS},
  author={Gunter Fuchs},
  journal={The Journal of Symbolic Logic},
  year={2018},
  volume={83},
  pages={283 - 325}
}
  • G. Fuchs
  • Published 1 March 2018
  • Economics
  • The Journal of Symbolic Logic
Abstract I analyze the hierarchies of the bounded resurrection axioms and their “virtual” versions, the virtual bounded resurrection axioms, for several classes of forcings (the emphasis being on the subcomplete forcings). I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for… 
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6 Citations

6 Citations

Citation Type

Citation Type

COMBINING RESURRECTION AND MAXIMALITY
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…
SUBCOMPLETE FORCING, TREES, AND GENERIC ABSOLUTENESS
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It is shown that subcomplete forcing cannot add a new branch to an ω1-tree, and the relationships between bounded forcing axioms, preservation of Aronszajn trees of height and widthπ1 and generic absoluteness of ${\rm{\Sigma }}_1^1$-statements over first order structures of sizeπ1 are explored.
Canonical fragments of the strong reflection principle
  • 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:…
Virtual large cardinals
Subcomplete forcing principles and definable well‐orders
TLDR
Enhanced version of bounded forcing axioms are introduced that are strong enough to have the implications of the maximality principles mentioned above.
Diagonal reflections on squares
TLDR
It is shown that a diagonal reflection principle, DSR, implies the failure of weak threaded square principles, for every regular $$\lambda >\omega _1$$λ>ω1, and that this result is sharp.

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  • Economics
    The Journal of Symbolic Logic
  • 2018
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