5 papers
Set-theoretic inevitability
Chris Scambler, Cesare Straffelini
After defining the concept of inevitability for statements with the modal logic of forcing, we raise the question of which statements are inevitable under and under…
Simultaneous Sequential Compactness
Sirio Resteghini, Cesare Straffelini
A set of sequences is said to converge simultaneously if there exists an infinite subset of the index set such that all sequences converge when restricted to . We discus…
Terminal Absoluteness of Collapse Forcings
Cesare Straffelini
Generic absoluteness is the phenomenon that certain truths in the set-theoretic universe remain stable under forcing expansions. A classical result by Kripke asserts that every com…
Higher Solovay Models
Cesare Straffelini, Sebastiano Thei
We introduce an axiomatisation of when a model of the form can be considered a ``-Solovay model''; we show a characterisation of -Solovay models; and we prove…
Minimal Banach-Tarski decompositions
Cesare Straffelini, Kilian Zambanini
We investigate the problem of finding the minimum number of pieces necessary for dividing a three-dimensional sphere or a ball and reassembling it to form congruent copies of t…