Related papers: Trees of tangles in abstract separation systems
We show that if a graph admits a packing and a covering both consisting of $\lambda$ many spanning trees, where $\lambda$ is some infinite cardinal, then the graph also admits a decomposition into $\lambda$ many spanning trees. For finite…
We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
We study triangle decompositions of graphs. We consider constructions of classes of graphs where every edge lies on a triangle and the addition of the minimum number of multiple edges between already adjacent vertices results in a strongly…
Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…
In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to…
A semantic tableau method, called an argumentation tableau, that enables the derivation of arguments, is proposed. First, the derivation of arguments for standard propositional and predicate logic is addressed. Next, an extension that…
This is a new and short proof of the main theorem of classical structure tree theory. Namely, we show the existence of certain automorphism-invariant tree-decompositions of graphs based on the principle of removing finitely many edges. This…
A theorem of alternatives provides a reduction of validity in a substructural logic to validity in its multiplicative fragment. Notable examples include a theorem of Arnon Avron that reduces the validity of a disjunction of multiplicative…
We describe a completely algebraic axiom system for intertwining operators of vertex algebra modules, using algebraic flat connections, thus formulating the concept of a {\em tree algebra}. Using the Riemann-Hilbert correspondence, we…
We show some basic facts about dp-minimal ordered structures. The main results are : dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure…
Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements &…
We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already,…
This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…
This paper develops a proof-theoretic framework for abstract interpretation by systematically associating logical systems with finite abstractions. Building on earlier work on the internal logics of abstractions, we propose a general…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
The study of representations of affine Hecke algebras has led to a new notion of shapes and standard Young tableaux which works for the root system of any finite Coxeter group. This paper is completely independent of affine Hecke algebra…
In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…
Reduction trees are a way of encoding a substitution procedure dictated by the relations of an algebra. We use reduction trees in the subdivision algebra to construct canonical triangulations of flow polytopes which are shellable. We…
Tangles of graphs have been introduced by Robertson and Seymour in the context of their graph minor theory. Tangles may be viewed as describing "k-connected components" of a graph (though in a twisted way). They play an important role in…