Currently, the most popular views about how to update de se or self-locating beliefs entail the one-third solution to the Sleeping Beauty problem. 2 Another widely held view is that an agent‘s credences should be countably additive. 3 In what follows, I will argue that there is a deep tension between these two positions. For the assumptions that underlie the one-third solution to the Sleeping B...

Let (Ω,F,P) be a probability space and L0(F) the algebra of equivalence classes real-valued random variables defined on (Ω,F,P). A left module M over (briefly, an L0(F)-module) is said to regular if x=y for any given two elements x y in such that there exists countable partition {An,n∈N} Ω F I˜An⋅x=I˜An⋅y each n∈N, where IAn characteristic function An I˜An its class. The purpose this paper esta...

1 . Introduction . The following question was posed by D . Maharam : Can one divide the unit square into two or more measurable sets each of which has a non-null intersection with every product set A XB of positive measure, where A and B are subsets of the unit interval? In this paper we construct a class of such partitions of the plane, including some that retain the property under various tra...

Motivated by Tukey classification problems and building on work in [4], we develop a new hierarchy of topological Ramsey spaces Rα, α < ω1. These spaces form a natural hierarchy of complexity, R0 being the Ellentuck space [6], and for each α < ω1, Rα+1 coming immediately afterRα in complexity. Associated with each Rα is an ultrafilter Uα, which is Ramsey for Rα, and in particular, is a rapid p-...

A graph property is any nonempty isomorphism-closed class of simple (finite or infinite) graphs. A graph property P is of finite character if a graph G has a property P if and only if every finite induced subgraph of G has a property P . Let P1,P2, . . . ,Pn be graph properties of finite character, a graph G is said to be (uniquely) (P1,P2, . . . ,Pn)partitionable if there is an (exactly one) p...

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that b...

We investigate the polynomial time isomorphic type structure of PT ⊂ {A : A ⊆ {0}∗} (the class of tally, polynomial time computable sets). We partition PT into six parts: D−, D̂−, C, S, F, F̂ , and study their p-isomorphic properties separately. The structures of 〈deg1(F ); ≤〉, 〈deg1(F̂ ); ≤〉, and 〈deg1(C); ≤〉 are obvious, where F , F̂ , and C are the class of tally finite sets, the class of tally ...