Related papers: On many-sorted $\omega$-categorical theories

We prove that arithmetic is interpretable in any indecomposable polynomial ring (in any set of variables), and in addition we provide an alternative uniform proof of undecidability for all members in this class of rings.

Lindstr\"om's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward L\"owenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious…

We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…

In is paper we present a labelled tableau proof system that serves a wide class of interpretability logics. The system is proved sound and complete for any interpretability logic characterised by a frame condition given by a set of…

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.

A classification is given of all the countable homogeneous ordered bipartite graphs.

We study the sets of the infinite sentences constructible with a dictionary over a finite alphabet, from the viewpoint of descriptive set theory. Among other things, this gives some true co-analytic sets. The case where the dictionary is…

We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…

It is well known that strict $\omega$-categories, strict $\omega$-functors, strict natural $\omega$-transformations, and so on, form a strict $\omega$-category. A similar property for weak $\omega$-categories is one of the main hypotheses…

We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense…

First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…

We prove that the Baire Category Theorem is equivalent to the following: Let G be a topological groupoid such that the unit space is a complete metric space, and there is a countable cover of G by neighbourhood bisections. If G is…

We show that in a weak globular $\omega$-category, all composition operations are equivalent and commutative for cells with sufficiently degenerate boundary, which can be considered a higher-dimensional generalisation of the Eckmann-Hilton…

Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.

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…

We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ is a predicate on $D$. In particular we show: (a) The set of recursive…

We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More generally, we calculate the number of equivalence classes of…

We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…

A set $G \subseteq \omega$ is $n$-generic for a positive integer $n$ if and only if every $\Sigma^0_n$ formula of $G$ is decided by a finite initial segment of $G$ in the sense of Cohen forcing. It is shown here that every $n$-generic set…

Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…