Related papers: Lov\'asz Theorems for Modal Languages

We show that the mod $\ell$ cohomology of any finite group of Lie type in characteristic $p$ different from $\ell$ admits the structure of a module over the mod $\ell$ cohomology of the free loop space of the classifying space $BG$ of the…

In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite…

We present a model-theoretic property of finite structures, that can be seen to be a finitary analogue of the well-studied downward L\"owenheim-Skolem property from classical model theory. We call this property as the…

We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…

A canonical result in model theory is the homomorphism preservation theorem (h.p.t.) which states that a first-order formula is preserved under homomorphisms iff it is equivalent to an existential-positive formula, standardly proved via a…

We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T. We show that all sufficiently large…

Throughout, $T$ denotes a complete first-order theory in a countable language $L$ that has infinite models and $I(\aleph_0,T)$ denotes the number of countable models of $T$, up to an isomorphism. To determine $I(\aleph_0,T)$, it suffices to…

We prove preservation theorems for $\mathcal{L}_{\omega_1, G}$, the countable fragment of Vaught's closed game logic. These are direct generalizations of the theorems of \L{}o\'s-Tarski (resp. Lyndon) on sentences of $\mathcal{L}_{\omega_1,…

We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…

A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…

Let $\mathrm{XY_{L,T}}$ denote the class of countably infinite $L$-structures that satisfy the axioms $T$ and in which all homomorphisms of type X (these could be homomorphisms, monomorphisms, or isomorphisms) between finite substructures…

We present an example of two countable $\omega$-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids -- in other words, no…

We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical…

We show that if we enrich first order logic by allowing quantification over isomorphisms between definable ordered fields the resulting logic, L(Q_{Of}), is fully compact. In this logic, we can give standard compactness proofs of various…

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…

We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the chains of homomorphisms $M_0 \stackrel{f_1}{\rightarrow} M_1…

Local-order-invariant (first-order) logic is an extension of first-order logic where formulae have access to a ternary local order relation on the Gaifman graph, provided that the truth value does not depend on the specific order relation…

Let L be a countable language. We say that a countable infinite L-structure M admits an invariant measure when there is a probability measure on the space of L-structures with the same underlying set as M that is invariant under…

I investigate modal group theory for arbitrary homomorphisms. Possibility is interpreted by the existence of a group homomorphism out of the given group, so the semantics is governed by the possibility of collapse: elements may be…

We study the Borel-reducibility of isomorphism relations of complete first order theories and show the consistency of the following: For all such theories T and T', if T is classifiable and T' is not, then the isomorphism of models of T' is…