Related papers: Dependent first order theories, continued
The randomization of a complete first order theory $T$ is the complete continuous theory $T^R$ with two sorts, a sort for random elements of models of $T$, and a sort for events in an underlying atomless probability space. We study…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
Ordinal pattern dependence is a multivariate dependence measure based on the co-movement of two time series. In strong connection to ordinal time series analysis, the ordinal information is taken into account to derive robust results on the…
A popular framework for false discovery control is the random effects model in which the null hypotheses are assumed to be independent. This paper generalizes the random effects model to a conditional dependence model which allows…
We prove that certain pairs of ordered structures are dependent. Among these structures are dense and tame pairs of o-minimal structures and further the real field with a multiplicative subgroup with the Mann property, regardless of whether…
The theory of fields that are equipped with a countably infinite family of commuting derivations is not companionable; but if the axiom is added whereby the characteristic of the fields is zero, then the resulting theory is companionable.…
We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…
A complete first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition.…
Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…
One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…
For a dependent theory T, in C_T for every type definable group G, the intersection of type definable subgroups with bounded index is a type definable subgroup with bounded index.
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this paper, using the concept of patterns of consistency…
Let $X$ be a max-stable random vector with positive continuous density. It is proved that the conditional independence of any collection of disjoint sub-vectors of $X$ given the remaining components implies their joint independence. We…
Let K be an algebraically bounded structure and T be its theory. If T is model complete, then the theory of K endowed with a derivation, denoted by $T^{\delta}$, has a model completion. Additionally, we prove that if the theory T is…
In this article we provide a substantial discussion on the statistical concept of conditional independence, which is not routinely mentioned in most elementary statistics and mathematical statistics textbooks. Under the assumption of…
String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in…
Throughout, $T$ denotes a complete first-order theory in a countable language $L$ that has infinite models and $I(\aleph_0,T)$ denotes the number of countable models of $T$, up to an isomorphism. To determine $I(\aleph_0,T)$, it suffices to…
We study the coherence and conservativity of extensions of dependent type theories by additional strict equalities. By considering notions of congruences and quotients of models of type theory, we reconstruct Hofmann's proof of the…
We introduce a new definition of topological degree for a meaningful class of operators which need not be continuous. Subsequently, we derive a number of fixed point theorems for such operators. As an application, we deduce a new existence…