7 citations · 12 across the 12 of their papers we have counts for
14 papers
Products of Classes of Finite Structures
Vince Guingona, Miriam Parnes, Lynn Scow
We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamatio…
Littlestone and VC-dimension of families of zero sets
Vincent Guingona, Alexei Kolesnikov, Julie Nierwinski +1
We prove that, for any linearly independent functions from some set into a -dimensional vector space over any field, the family of zero sets of all non-trivial linear combin…
On positive local combinatorial dividing-lines in model theory
Vincent Guingona, Cameron Donnay Hill
We introduce the notion of positive local combinatorial dividing-lines in model theory. We show these are equivalently characterized by indecomposable algebraically trivial Fraisse…
Characterizing Model-Theoretic Dividing Lines via Collapse of Generalized Indiscernibles
Vincent Guingona, Cameron Donnay Hill, Lynn Scow
We use the notion of collapse of generalized indiscernible sequences to classify various model theoretic dividing lines. In particular, we use collapse of n-multi-order indiscernib…
On VC-density in VC-minimal theories
Vincent Guingona
We show that any formula with two free variables in a VC-minimal theory has VC-codensity at most two. Modifying the argument slightly, we give a new proof of the fact that, in a VC…
On VC-minimal fields and dp-smallness
Vincent Guingona
In this paper, we show that VC-minimal ordered fields are real closed. We introduce a notion, strictly between convexly orderable and dp-minimal, that we call dp-small, and show th…
On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension
Vincent Guingona, Cameron Donnay Hill
In this paper, we build a dimension theory related to Shelah's 2-rank, dp-rank, and o-minimal dimension. We call this dimension op-dimension. We exhibit the notion of the n-multi-o…
Convexly orderable groups and valued fields
Joseph Flenner, Vincent Guingona
We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, ho…
Canonical forests in directed families
Joseph Flenner, Vincent Guingona
Two uniqueness results on representations of sets constructible in a directed family of sets are given. In the unpackable case, swiss cheese decompositions are unique. In the packa…
On VC-minimal theories and variants
Vincent Guingona, Michael C. Laskowski
In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablility and show that this lies strictly between VC-minimality…
Definability of types over finite partial order indiscernibles
Vincent Guingona
In this paper, we show that a partitioned formula ϕis dependent if and only if ϕhas uniform definability of types over finite partial order indiscernibles. This generalizes our res…
On VC-density over indiscernible sequences
Vincent Guingona, Cameron Donnay Hill
In this paper, we study VC-density over indiscernible sequences (denoted VC_ind-density). We answer an open question in [1], showing that VC_ind-density is always integer valued. W…
On uniform definability of types over finite sets
Vincent Guingona
In this paper, using definability of types over indiscernible sequences as a template, we study a property of formulas and theories called "uniform definability of types over finit…
Dependence and Isolated Extensions
Vincent Guingona
In this paper, we show that ϕis a dependent formula if and only if all ϕ-types have an extension to a ϕ-isolated ϕ-type that is an "elementary ϕ-extension" (see Definition 2.3 in t…