Related papers: Some definable types that cannot be amalgamated

We characterize trees as median algebras and semilattices by relaxing conservativeness. Moreover, we describe median homomorphisms between products of median algebras and show that Arrow type impossibility theorems for mappings from a…

We provide here the first steps toward Classification Theory of Abstract Elementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is categorical in some lambda greater than its Lowenheim-Skolem…

We propose a new cubical type theory, termed (self-deprecatingly) the naive cubical type theory, and study its semantics using the universe category framework, which is similar to Uemura's categories with representable morphisms. In…

We construct inner amenable groups G with infinite conjugacy classes and such that the associated II_1 factor does not have property Gamma of Murray and von Neumann. This solves a problem posed by Effros in 1975.

We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We…

We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…

A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…

In this work we characterize the combinatorial metrics admitting a MacWilliams-type identity and describe the group of linear isometries of such metrics. Considering coverings that are not connected, we classify the metrics satisfying the…

We show that it is impossible to classify topological conjugacy relation of minimal homeomorphisms on the torus by countable structures.

We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not…

We prove "untyping" theorems: in some typed theories (semirings, Kleene algebras, residuated lattices, involutive residuated lattices), typed equations can be derived from the underlying untyped equations. As a consequence, the…

We extend a recent result of McKenzie, and show that it is an undecidable problem to determine if 4 appears in the typeset of a finitely generated, locally finite variety.

We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside…

Adapting a claim of M. Kracht, we establish a characterization of the typable partial applicative algebras.

We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the…

We construct uncountably categorical 3-nilpotent groups of exponent p > 3. They are not one-based and do not allow the interpretation of an infinite field. Therefore they are counterexamples to Zilbers Conjecture. First 2-nilpotent new…

(withdrawn.) For every lambda we give an explicit construction of an Abelian group with no non-trivial automorphisms. In particular the group absolutely has no non-trivial automorphisms, hence is absolutely indecomposable. Earlier we knew a…

We study the decidability of the topological properties of some objects coming from fractal geometry. We prove that having empty interior is undecidable for the sets defined by two-dimensional graph-directed iterated function systems. These…

We define a class of algebras describing links of binary isolating formulas on a set of realizations for a family of 1-types of a complete theory. We prove that a set of labels for binary isolating formulas on a set of realizations for a…

Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…