16 citations · 37 across the 11 of their papers we have counts for
15 papers
Quantitative analytic stable regularity
G. Conant, C. Terry
We prove quantitative stable regularity lemmas for binary real-valued functions, extending the work of Malliaris and Shelah for stable graphs. The statements of our results are mod…
Pseudofinite proofs of the stable graph regularity lemma
G. Conant, C. Terry
This expository article is based on two lectures given by the first author at the Fields Institute in the Fall 2021 Thematic Program on Trends in Pure and Applied Model Theory. We…
Higher arity stability and the functional order property
A. Abd-Aldaim, G. Conant, C. Terry
The -dimensional functional order property () is a combinatorial property of a -partitioned formula. This notion arose in work of Terry and Wolf, which iden…
Higher-order generalizations of stability and arithmetic regularity
C. Terry, J. Wolf
We define a natural notion of higher order stability and show that subsets of that are tame in this sense can be approximately described by a union of low-complexi…
Irregular triads in 3-uniform hypergraphs
C. Terry, J. Wolf
Over the past several years, numerous authors have explored model theoretically motivated combinatorial conditions that ensure that a graph has an efficient regular decomposition i…
Jumps in speeds of hereditary properties in finite relational languages
Michael C. Laskowski, Caroline A. Terry
Given a finite relational language , a hereditary -property is a class of finite -structures closed under isomorphism and substructure. The s…
Uniformly bounded arrays and mutually algebraic structures
Michael C. Laskowski, Caroline A. Terry
We define an easily verifiable notion of an atomic formula having uniformly bounded arrays in a structure . We prove that if is a complete -theory, then is mutually a…
Stable arithmetic regularity in the finite-field model
C. Terry, J. Wolf
The arithmetic regularity lemma for , proved by Green in 2005, states that given a subset , there exists a subspace $H\leq \mathbb{F}_p^n…
-dimension and the jump to the fastest speed of a hereditary -property
C. Terry
In this paper we investigate a connection between the growth rates of certain classes of finite structures and a generalization of -dimension called -d…
Extremal theory of locally sparse multigraphs
Dhruv Mubayi, Caroline Terry
An -graph is an -vertex multigraph where every set of vertices spans at most edges. In this paper, we determine the maximum product of the edge multiplicities i…
An extremal graph problem with a transcendental solution
Dhruv Mubayi, Caroline Terry
We prove that the number of multigraphs with vertex set such that every four vertices span at most nine edges is where is transcendental (…
Structure and enumeration theorems for hereditary properties in finite relational languages
Caroline Terry
Given a finite relational language $\calL$, a hereditary $\calL$-property is a class of finite $\calL$-structures which is closed under isomorphism and model theoretic substructure…
On unavoidable induced subgraphs in large prime graphs
M. Malliaris, C. Terry
Chudnovsky, Kim, Oum, and Seymour recently established that any prime graph contains one of a short list of induced prime subgraphs [1]. In the present paper we reprove their theor…
Discrete metric spaces: structure, enumeration, and - laws
Dhruv Mubayi, Caroline Terry
Fix an integer . We consider metric spaces on points such that the distance between any two points lies in . Our main result describes their approximate…
Model theoretic properties of the Urysohn sphere
Gabriel Conant, Caroline Terry
We characterize model theoretic properties of the Urysohn sphere as a metric structure in continuous logic. In particular, our first main result shows that the theory of the Urysoh…