arXiv subjects

Pedro Zambrano

Publications and source records attributed to Pedro Zambrano.

6 recordsLinked to original sources

arXiv2022

Tameness in generalized metric structures

We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways, chiefly by allowing the metric to take values in a well-behaved quantale. As a proof of concept we show that the result of Boney and Zambrano on (metric) tameness under a large cardinal assumption holds in this more general context. We briefly consider a further generalization to partial metric spaces, and hint at connections to classes of fuzzy structures, and structures on sheaves.

math.LO↗

arXiv2015

Around the set-theoretical consistency of d-tameness of Metric Abstract Elementary Classes

In this paper, we prove that if $κ$ is a almost strongly compact cardinal, then any MAEC with Löwenheim-Skolem number below $κ$ is $<κ$-d-tame.

math.LO↗

arXiv2015

Towards a proof of the Shelah Presentation Theorem in Metric Abstract Elementary Classes

In my PhD thesis a version of Shelah's Presentation Theorem in the setting of Metric Abstract Elementary Classes was proved, where we claimed that the new function symbols are not necessarily uniformly continuous. In this paper we provide a proof they are in fact uniformly continuous.

math.LO↗

arXiv2015

Limit Models in Metric Abstract Elementary Classes: the Categorical case

We study versions of limit models adapted to the context of *metric abstract elementary classes*. Under categoricity and superstability-like assumptions, we generalize some theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context.

math.LO↗

arXiv2013

Around Independence and Domination in Metric Abstract Elementary Classes, under Uniqueness of Limit Models

We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case, and adapt definitions to the metric case. In particular, we study notions that behave well under superstability-like assumptions. Also, under uniqueness of limit models, we study domination, orthogonality and parallelism of Galois types in MAECs.

math.LO↗

arXiv2011

A stability transfer theorem in d-tame Metric Abstract Elementary Classes

In this paper, we study a stability transfer theorem in d-tame Metric Abstract Elementary classes, in a similar way as in [BaKuVa], but using superstability-like assumptions which involves a new independence notion (Tame Independence) instead of $\aleph_0$-locality.

math.LO↗