Related papers: Duality and the pcf theory

We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent…

We consider the class of physical theories whose dynamics are given by natural equations, which are partial differential equations determined by a functor from the category of n-manifolds, for some n, to the category of fiber bundles,…

This paper explores the options available to the anti-realist to defend a Quinean empirical under-determination thesis using examples of dualities. I first explicate a version of the empirical under-determination thesis that can be brought…

On the real numbers, the notions of a semi-decidable relation and that of an effectively enumerable relation differ. The second only seems to be adequate to express, in an algorithmic way, non deterministic physical theories, where…

In a large class of chiral gauge theories in four dimensions it was found that certain natural assumption about the bifermion condensates leads to the infrared effective theory where the 't Hooft anomaly matching conditions are satisfied in…

We study the connection between probability distributions satisfying certain conditional independence (CI) constraints, and point and line arrangements in incidence geometry. To a family of CI statements, we associate a polynomial ideal…

We show that every countable ideal of degrees that are low for isomorphism is contained in a principal ideal of degrees that are low for isomorphism by adapting an exact pair construction. We further show that within the hyperimmune-free…

We try to control many cardinal characteristics by working with a notion of orthogonality between two families of forcings. We show that b^+<g is consistent

We use forcing over admissible sets to show that, for every ordinal $\alpha$ in a club $C\subset\omega_1$, there are copies of $\alpha$ such that the isomorphism between them is not computable in the join of the complete $\Pi^1_1$ set…

Hidden-variable models aim to reproduce the results of quantum theory and to satisfy our classical intuition. Their refutation is usually based on deriving predictions that are different from those of quantum mechanics. Here instead we…

An inaccessible cardinal kappa is supercompact when (kappa, lambda)-ITP holds for all lambda greater than or equal to kappa. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC…

For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the…

Many tasks in statistical and causal inference can be construed as problems of \emph{entailment} in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for \emph{causal}…

We isolate a combinatorial property of capacities leading to a construction of proper forcings. Then we show that many classical capacities such as the Newtonian capacity satisfy the property.

We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditions on a matrix whose entries are probabilities of events…

Let $\FF$ be a finite field of characteristics different from two. We show that no bijective map transforms permanent into determinant when the cardinality of $\FF$ is sufficiently large. We also give an example of non-bijective map when…

Denote by $\continuum=2^{\aleph_0}$ the cardinal of continuum. We construct an intriguing family $(P_\alpha: \alpha\in\continuum)$ of prime $z$-ideals in $\C_0(\reals)$ with the following properties: If $f\in P_{i_0}$ for some…

C-cross topologies are introduced. Modifcations of the Kuratowski-Ulam Theorem are considered. Cardinal invariants add, cof, cov and non with respect to meager or nowhere dense subsets are compared. Remarks on invariants cof(nwdY) are…

We make use of some observations on the core model, for example assuming $V=L [ E ]$, and that there is no inner model with a Woodin cardinal, and $M$ is an inner model with the same cardinals as $V$, then $V=M$. We conclude in this latter…

Causality imposes strong restrictions on the type of operators that may be observables in relativistic quantum theories. In fact, causal violations arise when computing conditional probabilities for certain partial causally connected…