Fr\'echet completions of moderate growth old and (somewhat) new results

This article has two objectives. The first is to give a guide to the proof of the (so-called) Casselman-Wallach theorem as it appears in Real Reductive Groups II. The emphasis will be on one aspect of the original proof that leads to the new result in this paper which is the second objective. We show how a theorem of van der Noort combined with a clarification of the original argument in my book lead to a theorem with parameters (an alternative is one announced by Berstein and Kr\"otz). This result gives a new proof of the meromorphic continulation of the smooth Eisenstein series

Alternative Experimental Protocol for a PBR-Like Result

Pusey, Barrett and Rudolph (PBR) have recently proven an important new theorem in the foundations of quantum mechanics. Here we propose alternative experimental protocols which lead to the PBR result for a special case and a weaker PBR-like result generally. Alternative experimental protocols support the assumption of measurement independence required for the PBR theorem.Comment: 4 pages, 1 figur

Arrow's impossibility theorem: Two simple single-profile versions

In this short paper we provide two simple new versions of Arrow's impossibility theorem, in a world with only one preference profile. Both versions are extremely transparent. The first version assumes a two-agent society; the second version, which is similar to a theorem of Pollak, assumes two or more agents. Both of our theorems rely on diversity of preferences axioms, and we explore alternative notions of diversity at length. Our first theorem also uses a neutrality assumption, commonly used in the literature; our second theorem uses a neutrality/monotonicity assumption, which is stronger and less commonly used. We provide examples to show the logical independence of the axioms, and to illustrate our points.Arrow's theorem; single-profile