arXiv subjects

Camilo Argoty

Publications and source records attributed to Camilo Argoty.

5 recordsLinked to original sources

arXiv2023

SB-property on metric structures

A complete theory $T$ has the Schr\"oder-Bernstein property or simply the SB-property if any pair of elementarily bi-embeddable models are isomorphic. This property has been studied in the discrete first-order setting and can be seen as a first step towards classification theory. This paper deals with the SB-property on continuous theories. Examples of complete continuous theories that have this property include Hilbert spaces and any completion of the theory of probability algebras. We also study a weaker notion, the SB-property up to perturbations. This property holds if any two elementarily bi-embeddable models are isomorphic up to perturbations. We prove that the theory of Hilbert spaces expanded with a bounded self-adjoint operator has the SB-property up to perturbations of the operator and that the theory of atomless probability algebras with a generic automorphism have the SB-property up to perturbations of the automorphism. We also study how the SB-property behaves with respect to randomizations. Finally we prove, in the continuous setting, that if $T$ is a strictly stable theory then $T$ does not have the SB-property.

math.LO↗

arXiv2012

Model theory of a non-degenerate representation of a unital C*-algebra

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are elementary equivalent to it. We show that for every v in H the type of v over the empmtyset is in correspondence with the positive linear functional over A defined by v and has quantifier elimination as well. Finally, we characterize the model companion of the incomplete theory of all non-degenerate representations of A.

math.LO↗

arXiv2012

Forking and stability in the representations of a C*-algebra

We show that the theory of a non-degenerate representation of a C*-algebra A over a Hilbert space H is superstable. Also, we characterize forking, orthogonality and domination of types and show that the theory has weak elimination of imaginaries.

math.LO↗

arXiv2011

A generalization of a classical model in contract theory: The agent behavior

We present a first approximation of agent behaviour in a generalized model in contract theory. This model relaxes some of the the assumptions of one of the classical models allowing to include a broader range of agents. We introduce the motivation for the agent and reinterpret the classical definition of risk perception. Besides, we analyze different scenarios for the relation between the effort exerted by the agent and the probability that he gets an especfic result.

math.OC↗

arXiv2011

Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator

We study a closed unbounded self-adoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECS). We build a suitable MAEC for (H,Q), prove it is aleph 0 stable up to perturbations and characterize non-splitting and show it has the same properties as non-forking in superstable first order theorues. Also, we characterize equality, orthogonality and domination of (Galois) types in that MAEC.

math.LO↗