相关论文: DOP and FCP in generic structures

For every fixed graph $H$ and every fixed $0 < \alpha < 1$, we show that if a graph $G$ has the property that all subsets of size $\alpha n$ contain the ``correct'' number of copies of $H$ one would expect to find in the random graph…

Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…

Ramsey theory looks for regularities in large objects. Model theory studies algebraic structures as models of theories. The structural Ramsey theory combines these two fields and is concerned with Ramsey-type questions about certain…

Originally introduced by Kolmann and Shelah as a surrogate for saturated models, limit models have been established as natural and useful objects when studying abstract elementary classes. Shelah began the study of when (multiple notions…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

This paper contributes to the set-theoretic side of understanding Keisler's order. We consider properties of ultrafilters which affect saturation of unstable theories: the lower cofinality $\lcf(\aleph_0, \de)$ of $\aleph_0$ modulo $\de$,…

We generalize a theory of Shelah for continuous logic, namely a continuous theory has OP if and only if it has IP or SOP.

We show that for a number of theories $T^*$ of model-theoretic interest there is a simpler theory $T$ and $\kappa \ge \aleph_0$ such that $T^*$ is trace equivalent to the theory of $\kappa$-dimensional space over a model of $T$.

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance…

We survey recent developments concerning two properties of classes of finite structures: the Ramsey property and the extension property for partial automorphisms (EPPA).

A result of Simonovits and S\'os states that for any fixed graph $H$ and any $\epsilon > 0$ there exists $\delta > 0$ such that if $G$ is an $n$-vertex graph with the property that every $S \subseteq V(G)$ contains $p^{e(H)} |S|^{v(H)} \pm…

Given a hereditary graph property $\mathcal{P}$, consider distributions of random orderings of vertices of graphs $G\in\mathcal{P}$ that are preserved under isomorphisms and under taking induced subgraphs. We show that for many properties…

We consider an evolving preferential attachment random graph model where at discrete times a new node is attached to an old node, selected with probability proportional to a superlinear function of its degree. For such schemes, it is known…

This paper studies higher index theory for a random sequence of bounded degree, finite graphs with diameter tending to infinity. We show that in a natural model for such random sequences the following hold almost surely: the coarse…

We study the Universal Difference Property (UDP) introduced by Alt{\i}nok, Anders, Arreola, Asencio, Ireland, Sar{\i}o\u{g}lan, and Smith, focusing on the relationship between the structural properties of a graph and UDP. We present…

We give several new characterizations of $IP$ (the independence property) and $SOP$ (the strict order property) for continuous first order logic and study their relations to the function theory and the Banach space theory. We suggest new…

In 1962, P\'osa conjectured that a graph $G=(V, E)$ contains a square of a Hamiltonian cycle if $\delta(G)\ge 2n/3$. Only more than thirty years later Koml\'os, S\'ark\H{o}zy, and Szemer\'edi proved this conjecture using the so-called…

We study model theoretic tree properties ($\text{TP}, \text{TP}_1, \text{TP}_2$) and their associated cardinal invariants ($\kappa_{\text{cdt}}, \kappa_{\text{sct}}, \kappa_{\text{inp}}$, respectively). In particular, we obtain a…

Scale-free networks are abundant in nature and society, describing such diverse systems as the world wide web, the web of human sexual contacts, or the chemical network of a cell. All models used to generate a scale-free topology are…

If T is an model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.