We prove that, under fairly general conditions, a properly rescaled de-terminantal random point field converges to a generalized Gaussian random process. 1. Introduction and formulation of results. Let E be a locally compact Hausdorff space satisfying the second axiom of countability, B—σ-algebra of Borel subsets and µ a σ-finite measure on (E, B), such that µ(K) < ∞ for any compact K ⊂ E. We d...

In my lecture at the 2011 Congress on Logic, Methodology, and the Philosophy of Science in Nancy, France, I spoke on an additional axiom of set theory — the Proper Forcing Axiom — which has proved very successful in settling combinatorial problems concerning uncountable sets. Since I have already written a exposition on this subject [43], I have decided to address a broader question in this art...

Let H 0(X) (H(X)) denote the set of all (nonempty) closed subsets of X endowed with the Vietoris topology. A basic problem concerning H(X) is to characterize those X for which H(X) is countably compact. We conjecture that u-compactness of X for some u ∈ ω∗ (or equivalently: all powers of X are countably compact) may be such a characterization. We give some results that point into this direction...

0. Introduction The issue of what is usually, but also misleadingly (see below) called the count-mass distinction, i.e. the grammatical distinction between nouns that can be counted (e.g. a car, two cars, many cars) and nouns that cannot (e.g. *a sand, *two sands, *many sands, sand, much sand), has been addressed and accounted for in different ways. This paper aims at giving a critical survey o...

Let us call a function f from a space X into a space Y preserving if the image of every compact subspace of X is compact in Y and the image of every connected subspace of X is connected in Y . By elementary theorems a continuous function is always preserving. Evelyn R. McMillan [6] proved in 1970 that if X is Hausdorff, locally connected and Frèchet, Y is Hausdorff, then the converse is also tr...

Oracle separation methods are used in cryptography to rule out blackbox reductions between cryptographic primitives. It is sufficient to find an oracle relative to which the base primitive exists but there are no secure instances of the constructed primitive. In practice, it is beyond our current reach to construct a fixed oracle with such properties for most of the reductions because it is dif...

The Melvil Dewey Decimal Classification system maps the human knowledge domains into a library classification decimal system, which means that the knowledge is discretized. The domains are countable similarly to how Cantor proved the countability of the fractions’ domain. The debate about the “inter-” and “multi-” disciplinary domains may also be extended into “sub-domains” or from another poin...

Some results are obtained on the group of rational points on elliptic curves over infinite algebraic number fields. A certain naturally defined class of Dedekind domains, elliptic Dedekind domains, are described and it is shown that every countable abelian group can be realized as the class group of an elliptic Dedekind domain. Introduction. Let E be an elliptic curve defined over a field K. Le...

In 1976, Robert Aumann published his widely influential mathematical formulation of the idea of “common knowledge” in [2]. This paper had a great impact in game theory, control theory, economics, and related fields because of the conclusions that it drew. Aumann’s main theorem stated that if two agents began with identical prior beliefs (i.e. unbiased relative to each other) and their posterior...

Given topological spaces Xt ÜT, and F and a function h from XXT to F which is continuous in x for each fixed ty there is associated with h a function h* from I t o F = F x , the space whose elements are the continuous functions from X to F. The function h* is defined as follows: h*(t)=ht, where ht(x)~h(x} t) for every x in X. The correspondence between h and h* is obviously one-to-one. Although...