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  1. 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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