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Symmetry for transfinite computability
Lorenzo Galeotti, Ethan S. Lewis, Benedikt Löwe
Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; w…
Moving up and down in the generic multiverse
Joel David Hamkins, Benedikt Löwe
We give a brief account of the modal logic of the generic multiverse, which is a bimodal logic with operators corresponding to the relations "is a forcing extension of" and "is a g…
Structural connections between a forcing class and its modal logic
Joel David Hamkins, George Leibman, Benedikt Löwe
The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, interpreting necessity as "in all forcing extensions" and p…
Solovay-type characterizations for forcing-algebras
Jörg Brendle, Benedikt Loewe
We give characterizations for the (in ZFC unprovable) sentences ``Every $\Sb{1}{2}$--set is measurable" and ``Every $\Db{1}{2}$--set is measurable" for various notions of measurabi…
Uniform Unfolding and Analytic Measurability
Benedikt Loewe
We regard Forcing Notions P adding real numbers and the algebras of P-measurable sets. As for Cohen- and Random-Forcing we can show that each analytic set is P-measurable using Sol…