Related papers: Elementary submodels in infinite combinatorics
Additive combinatorics asks for lower bounds on sumsets and restricted sumsets over finite fields. Central examples are the Cauchy-Davenport theorem and the Erd\H{o}s-Heilbronn conjecture. In this note, we develop Das's linear algebraic…
Knowledge graphs are used to represent relational information in terms of triples. To enable learning about domains, embedding models, such as tensor factorization models, can be used to make predictions of new triples. Often there is…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
We present a mathematical framework for mapping second-order logic relations onto a simple state vector algebra. Using this algebra, basic theorems of set theory can be proven in an algorithmic way, hence by an expert system. We illustrate…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using $\sigma$-algebras, we define what a proof of a number-theoretical statement by Language Theory means. We prove…
A method is given for obtaining equivalence subgroups of a family of differential equations from the equivalence group of simpler equations of a similar form, but in which the arbitrary functions specifying the family element depend on…
We use high girth, high chromatic number hypergraphs to show that there are finite models of the equational theory of the semiring of nonnegative integers whose equational theory has no finite axiomatisation, and show this also holds if…
This contribution extends linear models for feature vectors to sublinear models for graphs and analyzes their properties. The results are (i) a geometric interpretation of sublinear classifiers, (ii) a generic learning rule based on the…
We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.
In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…
In this note, we use elementary submodels to prove that a separable monotonically normal compactum can be mapped on a separable metric space via a continuous function whose fibers have cardinality at most 2.
The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic…
We introduce the notion of pure extending modules, a refinement of classical extending modules in which only pure submodules are required to be essential in direct summands. Fundamental properties and characterizations are established,…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Wedderburn's theorem on the structure of finite dimensional semisimple algebras is proved by using minimal prerequisites.