Related papers: Some definable types that cannot be amalgamated

We give an example of a countable theory T such that for every cardinal lambda >= aleph_2 there is a fully indiscernible set A of power lambda such that the principal types are dense over A, yet there is no atomic model of T over A. In…

We give an example of an aleph-zero-categorical theory which is not G-compact. The countable model of this theory does not have AZ-enumerations.

We show that in a stable first-order theory, the failure of higher-dimensional type amalgamation can always be witnessed by algebraic structures which we call n-ary polygroupoids. This generalizes a result of Hrushovski that failures of…

We define a notion of a weak canonical base for a partial type. This notion is weaker than the usual canonical base for an amalgamation base. We prove that certain family of partial types have a weak canonical base. This family clearly…

We show that irreducibility is not a first-order definable property of real algebraic varieties. The proof is based on the recent o-minimality result for the exponential function. We conjecture that irreducibility is not a definable…

We consider the logic space of countable (enumerated) groups and show that closed subspaces corresponding to some standard classes of groups have (do not have) generic groups. We also discuss the cases of semigroups and associative rings.

We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…

We provide conditions under which the union of two first-order theories has the amalgamation property.

We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst non-forking types.

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

It is presented an example of a holomorphic foliation of a non-algebraizable surface which is topologically equivalent to an algebraic foliation.

We give a model of dependent type theory with one univalent universe and propositional truncation interpreting a type as a stack, generalising the groupoid model of type theory. As an application, we show that countable choice cannot be…

We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…

The title theorem is proved by example: an algebra of binary relations, closed under intersection and composition, that is not isomorphic to any such algebra on a finite set.

We find new "reasons" for a class of models for not having a universal model in a cardinal $\lambda$. This work, though it has consequences in model theory, is really in combinatorial set theory. We concentrate on a prototypical class which…

We construct a finitely generated group that does not satisfy the generalized Burghelea conjecture.

The two model-theoretic concepts of weak saturation and weak amalgamation property are studied in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly…

A generic extension $L[x]$ of $L$ by a real $x$ is defined, in which the $\mathsf E_0$-class of $x$ is a lightface $\Pi^1_2$ set containing no ordinal-definable reals.

We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…