Paulo Soto - Personal Website

About me

I am a 4^th year mathematics PhD student at Université Paris Cité and at the Équipe de Logique Mathématique of the Institut de Mathématiques de Jussieu-Paris Rive Gauche, under the supervision of Dr. Sylvy Anscombe. My main interests lie in the intersection of Model Theory and Algebra, namely in the Model Theory of Valued Fields and their classification theoretical properties (eg. NIP, NTP₂ and their variants).

I was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No 945332.

**Applying for postdocs to begin after september 2026**

You can find me at paulo.soto(at)imj-prg(dot)fr.

Here's a CV (Last updated: November 2025).

Preprints

Paulo Andrés Soto Moreno. Relative Quantifier Elimination for Separable-Algebraically Maximal Kaplansky Fields, Manuscript, 2025. Submitted.

Abstract: Let C be the class of separable-algebraically maximal equi-characteristic Kaplansky fields of a given imperfection degree, admitting an angular component map. We prove that the common theory of the class C resplendently eliminates quantifiers down to the residue field and the value group, in a three sorted language of valued fields with a symbol for an angular component map and symbols for the parameterized lambda-functions. As a consequence, we obtain that equi-characteristic NIP and NIPn henselian fields with an angular component map resplendently eliminate field quantifiers in this language. We also prove that this elimination reduces existential formulas to existential formulas without quantifiers from the home sort. Finally, we draw several conclusions following the AKE philosophy for elements of the class C, including the usual AKE principles for ≡, ≡∃, ⪯, ⪯∃ and for relative decidability.

Paulo Andrés Soto Moreno. Fields of dp-Rank 2 and their W₂-Topologies: The Characteristic 2 Case, Manuscript, 2025.

Abstract: In this note we reproduce Johnson's analysis of W₂-topologies on fields of characteristic 2, which was originally stated for fields of characteristic different than 2. Following his framework, we prove that the canonical topology of an unstable field of characteristic 2 and dp-rank at most 2 is a V-topology. Additionally, we show that any W₂-topology on a field of characteristic 2 is either induced by a the intersection of two valuation rings or it is induced by dense pre-diffeo-valuation data, completing the picture for all positive characteristic fields.

Work in Progress

Paulo Andrés Soto Moreno. NIP Fragments of Fields, Manuscript, 2025.

Abstract: In this note we study sets of NIP formulas in some theories of (valued) fields, with a special focus on the set of existential formulas. First, we prove a variant of a theorem of Johnson: every Σ-NIP valued field (i.e. a valued field whose existential formulas are NIP) of positive characteristic is henselian. Second, we give a new proof of the fact that Separably Closed Valued Fields of any characteristic and any imperfection degree are NIP, and use this result to fill some gaps of a proof of the so-called NIP Transfer Theorem for equi-characteristic henselian valued fields: such a valued field is NIP if and only if so is its residue field. Finally, we set the ground for the finer question of transfer of NIP formulas with bounded quantifier rank. Namely, we prove that a henselian equicharacteristic valued field is Σ_n-NIP (i.e. a valued field whose Σ_n-formulas are NIP) if and only if so is the residue field, conditional to a generalization of a well known statement about indiscernible sequences of singletons in valued fields. As a parallel strategy, we restate Poizat's coheir criterion for NIP theories into a statement about sets of NIP formulas Δ which are closed under boolean combinations: a theory T is Δ-NIP if and only if any Δ-type over a model admits at most 2^|T| global Δ-coheirs.

Education

Master 2 Logique Mathématique et Fondements de l'Informatique. Université Paris Cité, Paris, France. Mémoir: Inflators and Diffeo-valued Fields, supervised by Dr. Sylvy Anscombe.
Master's degre in Mathematics. Universidad de los Andes, Bogotá D.C., Colombia. Thesis: Dp-finite Hahn Series Fields, supervised by Dr. John Goodrick.
Bachelor's degree in Mathematics. Universidad de los Andes, Bogotá D.C., Colombia. Thesis: Keisler-Shelah's Theorem in Continuous Logic (in Spanish), supervised by Dr. Alexander Berenstein.

Teaching Experience

In French, at Université Paris Cité, Paris, France. I was a Teaching Assistant of the following courses:

Spring 2026: Analyse et Algèbre Linéaire, L2 CUPGE, Tavaux Dirigés.
Fall 2025: Logique et Suites, L1 MATH, Cours Magistral et Travaux Dirigés.
Fall 2025: Algèbre et Analyse 3, L2 MIASHS, Travaux Dirigés.
Spring 2025: Analyse et Algèbre Linéaire, Travaux Dirigés.
Spring 2025: Outils Bureautiques et Informatiques, Travaux Pratiques.
Fall 2023: Analyse et Algèbre Linéaire, Travaux Dirigés.
Fall 2023: Tutorat de Mathématiques.

In Spanish, at Universidad de los Andes, Bogotá D.C., Colombia. I was a Teaching Assistant of the following courses:

Spring 2021: Vector Calculus.
Fall 2020: Vector Calculus.
Spring 2020: Vector Calculus
Fall 2019: Differential Calculus, Precalculus.
Spring 2019: Topology.
Fall 2018: Mathematical Logic, Linear Algebra.
Spring 2018: Differential Calculus.
Spring 2017: Mathematical Logic.
Fall 2016: Differential Calculus.

I was also a Social Work Practice Educator at Universidad de los Andes, Bogotá D.C., during the Fall of 2017. I was in charge of organizing and teaching high-school contents to a group of students of Bogotá's school network in order to enhance their academic aptitudes and increase their chances to pursue a university career.

Conferences

Here are some conferences I have attended:

Model Theoretic Methods in Non-Archimedean Geometry - January 2025 - Münster (Germany)
Model Theory of Valued Fields and Applications - February 2024 - Lille (France)
GEOMOD Final Conference - November 2023 - Freibourg (Germany)
Model Theory of Valued Fields - May 2023 - CIRM - Marseille (France)