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Embedding orders into the cardinals with $D C_{κ}$

Asaf Karagila (2014)

Fundamenta Mathematicae

Jech proved that every partially ordered set can be embedded into the cardinals of some model of ZF. We extend this result to show that every partially ordered set can be embedded into the cardinals of some model of $Z F + D C_{< κ}$ for any regular κ. We use this theorem to show that for all κ, the assumption of $D C_{κ}$ does not entail that there are no decreasing chains of cardinals. We also show how to extend the result to and embed into the cardinals a proper class which is definable over the ground model. We use...

Equivariant measurable liftings

Nicolas Monod (2015)

Fundamenta Mathematicae

We discuss equivariance for linear liftings of measurable functions. Existence is established when a transformation group acts amenably, as e.g. the Möbius group of the projective line. Since the general proof is very simple but not explicit, we also provide a much more explicit lifting for semisimple Lie groups acting on their Furstenberg boundary, using unrestricted Fatou convergence. This setting is relevant to $L^{\infty}$ -cocycles for characteristic classes.

Erratum to the paper "The Axion of Choice, the Löwenheim–Skolem Theorem and Borel models" (Fund. Math. 137 (1991), 53-58)

J. Malitz, Jan Mycielski, W. Reinhardt (1992)

Fundamenta Mathematicae

Extension of Boolean homomorphisms with bounding semimorphisms.

Paul D. Bacsich (1972)

Journal für die reine und angewandte Mathematik

Displaying 1 – 4 of 4

Embedding orders into the cardinals with D C κ

Equivariant measurable liftings

Erratum to the paper "The Axion of Choice, the Löwenheim–Skolem Theorem and Borel models" (Fund. Math. 137 (1991), 53-58)

Extension of Boolean homomorphisms with bounding semimorphisms.

Currently displaying 1 – 4 of 4

Embedding orders into the cardinals with $D C_{κ}$