We sketch a brief development of large cardinals as they apply to determinacy results and to inner model theory.

In this note measures with finite index of determinacy (i.e. determinate measures μ for which there exists a polynomial p such that |p|2μ is indeterminate) are characterizated in terms of the operator associated to its Jacobi matrix. Using this characterization, we show that such determinate measures with finite index of determinacy (Jekyll) turn out to be indeterminate (Hyde) when considered a...

Metric spaces, Borel and analytic sets, Baire property and measurability, dichotomies, equivalence relations. Possible topics: determinacy, group actions, rigidity, turbulence.

The fact that data is scattered over many tables causes many problems in the practice of data mining. To deal with this problem, one either constructs a single table by propositionalisation, or uses a Multi-Relational Data Mining algorithm. In either case, one has to deal with the non-determinacy of one-to-many relationships. In propositionalisation, aggregate functions have already proven to b...

A fundamental theorem of Büchi and Landweber shows that the Church synthesis problem is computable. Büchi and Landweber reduced the Church Problem to problems about ω-games and used the determinacy of such games as one of the main tools to show its computability. We consider a natural generalization of the Church problem to countable ordinals and investigate games of arbitrary countable length....

Tomato plants harboring the ripening-inhibitor (rin) mutation yield fruits that fail to ripen. Additionally, rin plants display enlarged sepals and loss of inflorescence determinacy. Positional cloning of the rin locus revealed two tandem MADS-box genes (LeMADS-RIN and LeMADS-MC), whose expression patterns suggested roles in fruit ripening and sepal development, respectively. The rin mutation a...

For a given set of queries (which are expressions in some query language) Q = {Q1, Q2, . . . Qk} and for another query Q0 we say that Q determines Q0 if – informally speaking – for every database D, the information contained in the views Q(D) is sufficient to compute Q0(D). Query Determinacy Problem is the problem of deciding, for given Q and Q0, whether Q determines Q0. Many versions of this p...

The goal of this paper is to extend Morley’s results in [10] to categories of sheaves. We show that in this context there are four natural notions of “a countable model”. We then show Π3 determinacy implies that for any of these four notions and for any sentence T ∈ Lω1,ω(L) either there is a perfect set of non-isomorphic models of T in our category of sheaves or else there are at most א1 many ...

We study a cooperative system of integro-differential equations. It is shown that the system in general has multiple spreading speeds, and when the linear determinacy conditions are satisfied all the spreading speeds are the same and equal to the spreading speed of the linearized system. The existence of traveling wave solutions is established via integral systems. It is shown that when the lin...

We introduce the concept of topological finite-determinacy for germs analytic functions within a fixed ideal I, which provides a notion of topological finite-determinacy of functions with non-isolated singularities. We generalize classical results of Thom and Varchenko stating the following: let A be the complement in the ideal I of the space of germs whose topological type remains unchanged un...