Papers by Pedro H . Zambrano
arXiv: Logic, 2015
In my PhD thesis a version of Shelah's Presentation Theorem in the setting of Metric Abstract... more 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.
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arXiv: Logic, 2015
In this paper, we prove that if $\kappa$ is a almost strongly compact cardinal, then any MAEC wit... more In this paper, we prove that if $\kappa$ is a almost strongly compact cardinal, then any MAEC with L\"owenheim-Skolem number below $\kappa$ is $<\kappa$-d-tame.
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In this paper, we propose a generalization of Continuous Logic ([BBHU08]) where the distances tak... more In this paper, we propose a generalization of Continuous Logic ([BBHU08]) where the distances take values in suitable co-quantales (in the way as it was proposed in [Fla97]). By assuming suitable conditions (e.g., being co-divisible, co-Girard and a V-domain), we provide, as test questions, a proof of a version of the Tarski-Vaught test (Proposition 3.35) and Łoś Theorem (Theorem 3.62) in our setting.
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We broaden the framework of metric abstract elementary classes (mAECs) in several essential ways,... more 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.
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arXiv: Logic, 2018
We remark that forcing on fiber bundles of structures of first order languages is not a compatibl... more We remark that forcing on fiber bundles of structures of first order languages is not a compatible semantics with the pullback (of fiber bundles) and we describe a semantics which behaves well with respect to it. This new semantics uses parallel transport and allows to introduce two different types of extensions for the formulae: vertical and horizontal extensions.
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We study versions of limit models adapted to the context of metric abstract elementary classes. U... more We study versions of limit models adapted to the context of metric abstract elementary classes. Under superstability-like assumptions, we prove some generalizations of theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context. 1. Preliminaries Why limit models and towers? The Model Theory of metric structures can be approached in a fruitful way from the Abstract Elementary Class perspective — extending in some senses the framework of First Order ContinuousModel Theory [BeBeHeUs] and in other senses beneVtting from the enormous richness of the Stability Theory in Abstract Elementary Classes. Other authors (Hirvonen [Hi] in her thesis with Hyttinen, Usvyatsov and Shelah) have provided essentially two major frameworks for dealing with contexts outside “generalized Vrst order”. Hirvonen and Hyttinen have developed a solid framework for categoricity transfer of metric AEC and for the study ofא0-stable classes of metric structures (a good...
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Mathematical Logic Quarterly, 2016
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We prove that cats (compact abstract theories) satisfy a version of Tarski-Vaught test, a version... more We prove that cats (compact abstract theories) satisfy a version of Tarski-Vaught test, a version of DLST (downward Löwenheim-Skolem Tarski) theorem using density character instead of cardinality and the DAP property (disjoint amalgamation property.
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In this work we present some general categorial ideas on Abstract Elementary Classes (AECs) %\cit... more In this work we present some general categorial ideas on Abstract Elementary Classes (AECs) %\cite{She}, inspired by the totality of AECs of the form $(Mod(T), \preceq)$, for a first-order theory T: (i) we define a natural notion of (funtorial) morphism between AECs; (ii) explore the following constructions of AECs: "generalized" theories, pullbacks of AECs, (Galois) types as AECs; (iii) apply categorial and topological ideas to encode model-theoretic notions on spaces of types %(see Michael Lieberman Phd thesis) ; (iv) present the "local" axiom for AECs here called "local Robinson's property" and an application (Robinson's diagram method); (v) introduce the category $AEC$ of Grothendieck's gluings of all AECs (with change of basis); (vi) introduce the "global" axioms of "tranversal Robinson's property" (TRP) and "global Robinson's property" (GRP) and prove that TRP is equivalent to GRP and GRP entails a...
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Mathematical Logic Quarterly, 2014
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A. We study notions of independence appropriate for a stability theory of metric abstract element... more A. We study notions of independence appropriate for a stability theory of metric abstract elementary classes. We build on previous notions used in the discrete case, and adapt denitions to the metric case. In particular, we study notions that behave well under ...
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We remark that forcing on fiber bundles of structures of first order languages is not a compatibl... more We remark that forcing on fiber bundles of structures of first order languages is not a compatible semantics with the pullback (of fiber bundles) and we describe a semantics which behaves well with respect to it. This new semantics uses parallel transport and allows to introduce two different types of extensions for the formulae: vertical and horizontal extensions.
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We broaden the framework of metric abstract elementary classes
(mAECs) in several essential ways,... more We broaden the framework of metric abstract elementary classes
(mAECs) in several essential ways, chiefly by allowing the me
tric to take values in a well-behaved quantale. As a proof of concept we show that the result of [BZ15] 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.
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Math. Logic Q. 60 issue 3: 211–227, 2014. doi: 10.1002/malq.201300059, May 11, 2014
We study notions of independence appropriate for a stability theory of metric abstract elementary... more 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.
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In this paper, we study a stability transfer theorem in d-tame metric abstract elementary classes... more In this paper, we study a stability transfer theorem in d-tame metric abstract elementary classes, in a similar way as in 2, but using superstability-like assumptions which involves a new independence notion (ζ*-independence) instead of ℵ0-locality.
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Boletín de matemáticas, Jan 1, 2009
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"We study versions of limit models adapted to the context
of metric abstract elementary classes.... more "We study versions of limit models adapted to the context
of metric abstract elementary classes. Under superstability-like assumptions, we prove some generalizations of theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context."
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Papers by Pedro H . Zambrano
(mAECs) in several essential ways, chiefly by allowing the me
tric to take values in a well-behaved quantale. As a proof of concept we show that the result of [BZ15] 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.
of metric abstract elementary classes. Under superstability-like assumptions, we prove some generalizations of theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context."
(mAECs) in several essential ways, chiefly by allowing the me
tric to take values in a well-behaved quantale. As a proof of concept we show that the result of [BZ15] 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.
of metric abstract elementary classes. Under superstability-like assumptions, we prove some generalizations of theorems from [GrVaVi]. We prove criteria for existence and uniqueness of limit models in the metric context."
which hold in Covers of Multiplicative Groups of an Algebraically Closed
Field of characteristic 0, in order to study its model-theoretical be-
haviour using tools from the Model Theory of Non-Elementary Classes.