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  1. Subcomplete forcing principles and definable well‐orders.Gunter Fuchs - 2018 - Mathematical Logic Quarterly 64 (6):487-504.
    It is shown that the boldface maximality principle for subcomplete forcing,, together with the assumption that the universe has only set many grounds, implies the existence of a well‐ordering of definable without parameters. The same conclusion follows from, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that does not exist, for some, implies the existence of a well‐ordering of which is Δ1‐definable without parameters, and ‐definable (...)
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  • Subcomplete forcing, trees, and generic absoluteness.Gunter Fuchs & Kaethe Minden - 2018 - Journal of Symbolic Logic 83 (3):1282-1305.
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  • Errata: on the role of the continuum hypothesis in forcing principles for subcomplete forcing.Gunter Fuchs - forthcoming - Archive for Mathematical Logic:1-13.
    In this note, I will list instances where in the literature on subcomplete forcing and its forcing principles (mostly in articles of my own), the assumption of the continuum hypothesis, or that we are working above the continuum, was omitted. I state the correct statements and provide or point to correct proofs. There are also some new results, most of which revolve around showing the necessity of the extra assumption.
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  • Aronszajn tree preservation and bounded forcing axioms.Gunter Fuchs - 2021 - Journal of Symbolic Logic 86 (1):293-315.
    I investigate the relationships between three hierarchies of reflection principles for a forcing class $\Gamma $ : the hierarchy of bounded forcing axioms, of $\Sigma ^1_1$ -absoluteness, and of Aronszajn tree preservation principles. The latter principle at level $\kappa $ says that whenever T is a tree of height $\omega _1$ and width $\kappa $ that does not have a branch of order type $\omega _1$, and whenever ${\mathord {\mathbb P}}$ is a forcing notion in $\Gamma $, then it is (...)
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