Tootfinder

A Universe with a $\Delta^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $\Pi^1_n$-Uniformization
Stefan Hoffelner
https://arxiv.org/abs/2506.21778

A Universe with a $Δ^1_n$-definable well-order of the reals, $\mathsf{CH}$ and $Π^1_n$-Uniformization
This paper details the construction of a universe where $Π^1_3$-uniformization is true, the Continuum Hypothesis holds yet it possesses a $Δ^1_3$-definable well-order of its reals. The method can be lifted to canonical inner models with finitely many Woodin cardinals to produce universes of $\mathsf{CH}$, $Π^1_n$-uniformization and where additionally a $Δ^1_n$-definable well-order of the reals exist.

The Multiverse: a Philosophical Introduction
Jeremy Butterfield
https://arxiv.org/abs/2505.23639 https://arxiv.org/pdf/2505.23639

The Multiverse: a Philosophical Introduction
This book is a philosopher's introduction to the idea that our universe is just one of many universes. I present and assess three versions of the idea: one version from philosophy, and two from physics. In short, they are: all the logically possible worlds; all the branches of the quantum state, in an Everettian interpretation of quantum theory; and all the bubbles of inflationary cosmology. For each proposal, I choose one main philosophical question to discuss in depth. They are, respectively:…