# Continuous first order logic for unbounded metric structures

@article{Yaacov2008ContinuousFO,
title={Continuous first order logic for unbounded metric structures},
author={Itai Ben Yaacov},
journal={Journal of Mathematical Logic},
year={2008},
volume={08},
pages={197-223}
}
• I. Yaacov
• Published 1 December 2008
• Mathematics
• Journal of Mathematical Logic
We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach (which has been the common approach so far to Banach space structures in continuous logic), as well as of applying in situations where the unit ball approach does not apply (i.e. when the unit ball is not a definable set). We also introduce the process of single point…
In this thesis we prove a strong conceptual completeness result for first-order continuous logic. Strong conceptual completeness was proved in 1987 by Michael l\Iakkai' for classical first-order
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• I. Yaacov
• Mathematics
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• 2014
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• 2012
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## References

SHOWING 1-10 OF 11 REFERENCES

• Philosophy
• 2010
We develop continuous first order logic, a variant of the logic described by Chang and Keisler (1966). We show that this logic has the same power of expression as the framework of open Hausdorff
Abstract We prove that in a continuous ℵ0-stable theory every type-definable group is definable. The two main ingredients in the proof are: (i) Results concerning Morley ranks (i.e., Cantor-Bendixson
We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable,
• Mathematics
• 2008
A metric structure is a many-sorted structure with each sort a metric space, which for convenience is assumed to have finite diameter. Additionally there are functions (of several variables) between
We prove that in a continuous $\aleph_0$-stable theory every type-definable group is definable. The two main ingredients in the proof are: \begin{enumerate} \item Results concerning Morley ranks
• Mathematics
• 2008
Preface List of contributors 1. Conjugacy in groups of finite Morley rank Olivier Frecon and Eric Jaligot 2. Permutation groups of finite Morley rank Alexandre Borovik and Gregory Cherlin 3. A survey

### Ultraproducts in analysis, Analysis and Logic (Catherine Finet and Christian Michaux, eds.), London Mathematical Society

• Lecture Notes Series,
• 2002

### Measure Theory Volume 3: Measure Algebras

• Measure Theory Volume 3: Measure Algebras
• 2004

• 2004

### Model theory of normed fields, in preparation

• Model theory of normed fields, in preparation