Creature forcing and large continuum: The joy of halving

For $f,g\in\omega^\omega$ let $c^\forall_{f,g}$ be the minimal number of uniform $g$-splitting trees needed to cover the uniform $f$-splitting tree, i.e., for every branch $\nu$ of the $f$-tree, one of the $g$-trees contains $\nu$. Let $c^\exists_{f,g}$ be the dual notion: For every branch $\nu$, one of the $g$-trees guesses $\nu(m)$ infinitely often. We show that it is consistent that $c^\exists_{f_\epsilon,g_\epsilon}=c^\forall_{f_\epsilon,g_\epsilon}=\kappa_\epsilon$ for continuum many pairwise different cardinals $\kappa_\epsilon$ and suitable pairs $(f_\epsilon,g_\epsilon)$. For the proof we introduce a new mixed-limit creature forcing construction

Creation as an Ecumenical Problem: Renewed Belief through Green Experience

Loss of a sense of creaturehood and of members has occurred across the lines of divided churches in a secular context. The author explores the question whether green experience of nature can be a path toward a renewed sense of creaturehood. Bernard Lonergan’s distinction between faith and belief allows for identifying a primordial faith that interprets the cosmos as numinous. Ignatius of Loyola’s Spiritual Exercises interprets primordial faith with the biblical word of God as Creator. Why not develop local ecumenical experiments in reevangelization that address green experience

Even more simple cardinal invariants

Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.Comment: a few changes (minor corrections) from first versio

Prediction and explanation in the multiverse

Probabilities in the multiverse can be calculated by assuming that we are typical representatives in a given reference class. But is this class well defined? What should be included in the ensemble in which we are supposed to be typical? There is a widespread belief that this question is inherently vague, and that there are various possible choices for the types of reference objects which should be counted in. Here we argue that the ``ideal'' reference class (for the purpose of making predictions) can be defined unambiguously in a rather precise way, as the set of all observers with identical information content. When the observers in a given class perform an experiment, the class branches into subclasses who learn different information from the outcome of that experiment. The probabilities for the different outcomes are defined as the relative numbers of observers in each subclass. For practical purposes, wider reference classes can be used, where we trace over all information which is uncorrelated to the outcome of the experiment, or whose correlation with it is beyond our current understanding. We argue that, once we have gathered all practically available evidence, the optimal strategy for making predictions is to consider ourselves typical in any reference class we belong to, unless we have evidence to the contrary. In the latter case, the class must be correspondingly narrowed.Comment: Minor clarifications adde