We give a unified overview of the study of the effects of additional set theoretic axioms on
quotient structures. Our focus is on rigidity, measured in terms of existence (or rather non …

arxiv:math/9905016v2 [math.LO] 24 Jan 2000 Page 1 arxiv:math/9905016v2 [math.LO] 24
Jan 2000 THE MEASURE ALGEBRA DOES NOT ALWAYS EMBED ALAN DOW* AND KLAAS …

We study countable saturation of metric reduced products and introduce continuous fields of
metric structures indexed by locally compact, separable, completely metrizable spaces …

We extend the classical Feferman–Vaught theorem to logic for metric structures. This implies
that the reduced powers of elementarily equivalent structures are elementarily equivalent …

We prove that, under Martin's axiom, every-algebra of density character less than continuum
embeds into the Calkin algebra. Furthermore, we show that it is consistent with Zermelo …

arxiv:2407.20791v1 [math.LO] 30 Jul 2024 Page 1 arxiv:2407.20791v1 [math.LO] 30 Jul 2024
THE WEAK EXTENSION PRINCIPLE ALESSANDRO VIGNATI AND DENIZ YILMAZ Abstract …

We prove rigidity results for large classes of corona algebras, assuming the Proper Forcing
Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable …

We consider the Calkin algebra $\mathcal {Q}(\ell_2) $, ie, the quotient of the algebra
$\mathcal B (\ell_2) $ of all bounded linear operators on the separable Hilbert space $\ell_2 …

We prove several rigidity results for corona $ C^* $-algebras and\v {C} ech-Stone
remainders under the assumption of Forcing Axioms. In particular, we prove that a strong …

The purpose of this communication is to survey a theory of liftings, as developed in author's
thesis ([8]). The first result in this area was Shelah's construction of a model of set theory in …