# On d-finiteness in continuous structures

@article{Yaacov2007OnDI, title={On d-finiteness in continuous structures}, author={Itai Ben Yaacov and Alexander Usvyatsov}, journal={Fundamenta Mathematicae}, year={2007}, volume={194}, pages={67-88} }

We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite". Other…

## 37 Citations

### Reconstruction of non-$\aleph_0$-categorical theories

- Mathematics
- 2021

We generalise the correspondence between א0-categorical theories and their automorphism groups to arbitrary complete theories in classical logic, and to some theories (including, in particular, all…

### Omitting types in operator systems

- Mathematics
- 2015

We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next,…

### ALMOST INDISCERNIBLE SEQUENCES AND CONVERGENCE OF CANONICAL BASES

- MathematicsThe Journal of Symbolic Logic
- 2014

A model-theoretic account for several results regarding sequences of random variables appearing in Berkes and Rosenthal, and characterise types and notions of convergence of types as conditional distributions and weak/strong convergence thereof, and obtains the Main Theorem of Berke and Rosenthal.

### Existentially closed measure-preserving actions of free groups

- Mathematics
- 2022

This paper is motivated by the study of probability measure-preserving (pmp) actions of free groups using continuous model theory. Such an action is treated as a metric structure that consists of the…

### Measuring Dependence in Metric Abstract Elementary Classes with Perturbations Hirvonen,

- Mathematics

We de ne and study a metric independence notion in a homogeneous metric abstract elementary class with perturbations that is dp -superstable (superstable wrt. the perturbation topology), weakly…

### MEASURING DEPENDENCE IN METRIC ABSTRACT ELEMENTARY CLASSES WITH PERTURBATIONS

- MathematicsThe Journal of Symbolic Logic
- 2017

A way to measure the dependence of a tuple a from a set B over another set A and proves basic properties of the notion, e.g., that a is independent of B over A in the usual sense of homogeneous model theory if and only if the measure of dependence is < ε for all ε > 0.

### Categoricity in homogeneous complete metric spaces

- MathematicsArch. Math. Log.
- 2009

An analogue of Morley’s categoricity transfer theorem is proved and the framework of a homogeneous MAEC is defined were the existence of arbitrarily large models, joint embedding, amalgamation, homogeneity and a property which is called the perturbation property.

### Generic orbits and type isolation in the Gurarij space

- Mathematics
- 2012

We study the question of when the space of embeddings of a separable Banach space $E$ into the separable Gurarij space $\mathbf G$ admits a generic orbit under the action of the linear isometry group…

### On a Roelcke-precompact Polish group that cannot act transitively on a complete metric space

- MathematicsIsrael Journal of Mathematics
- 2018

We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that for certain Polish groups, namely Aut* (μ)…

### On a Roelcke-precompact Polish group that cannot act transitively on a complete metric space

- Mathematics
- 2018

We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that for certain Polish groups, namely Aut* (μ)…

## References

SHOWING 1-5 OF 5 REFERENCES

### Uncountable dense categoricity in cats

- MathematicsJournal of Symbolic Logic
- 2005

It is proved that under reasonable assumptions, every cat (compact abstract theory) is metric, and some of the theory of metric cats is developed.

### Countable models of stable theories

- Mathematics
- 1983

The notion of a normal theory is lntroduced, and it is proved that for such a theory T, J(t8, T) I or ? 8. We also include a short proof of Lachlan's theorem that for superstable T, J(8), T) = I or ?…

### Usvyatsov, Model theory for metric structures, Expanded lecture notes for a workshop given in March/April 2005, Isaac Newton Institute

- University of Cambridge,
- 2005

### Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex URL: http://math

- Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex URL: http://math

### Model-theoretic independence in the Banach lattices L p (µ), submitted

- Model-theoretic independence in the Banach lattices L p (µ), submitted