Related papers: Ranks for strongly dependent theories
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
In this note we prove and disprove some chain conditions in type definable and definable groups in dependent, strongly dependent and strongly^{2} dependent theories.
We consider sentence-definable and diagram-definable subfamilies of given families of theories, calculi for these subfamilies, as well dynamics and characteristics of these subfamilies with respect to rank and degree.
We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…
In this paper we give characterizations of the super-stable theories, in terms of an external property called representation. In the sense of the representation property, the mentioned class of first-order theories can be regarded as "not…
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…
We show that many definitions of stability found in the learning theory literature are equivalent to one another. We distinguish between two families of definitions of stability: distribution-dependent and distribution-independent Bayesian…
In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…
The (strong and weak) well-posedness is proved for singular SDEs depending on the distribution density point-wisely and globally, where the drift satisfies a local integrability condition in time-spatial variables, and is Lipschitz…
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
In extremal set theory our usual goal is to find the maximal size of a family of subsets of an $n$-element set satisfying a condition. A condition is called chain-dependent, if it is satisfied for a family if and only if it is satisfied for…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…
Positive dependencies have been compared in the literature under rather strong assumptions such as equality of conditional distributions, exchangeability, or stationarity. We establish supermodular ordering results for distributions that…
Just as Lascar's notion of abstract rank axiomatizes the U-rank, we propose axioms for the ranks $SU^d$ and $SU^f$, the foundation ranks of dividing and forking. We study the relationships between these axioms. As with superstable, we…
We propose a family of models to study the evolution of ties in a network of interacting agents by reinforcement and penalization of their connections according to certain local laws of interaction. The family of stochastic dynamical…
In this paper, the existence and uniqueness of strong solutions to distribution dependent neutral SFDEs are proved. We give the conditions such that the order preservation of these equations holds. Moreover, we show these conditions are…
Ranking entities such as algorithms, devices, methods, or models based on their performances, while accounting for application-specific preferences, is a challenge. To address this challenge, we establish the foundations of a universal…
In this paper, we consider one-to-one matchings between two disjoint groups of agents. Each agent has a preference over a subset of the agents in the other group, and these preferences may contain ties. Strong stability is one of the…