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About me
I am currently a researcher working as a project assistant associated with project P33895, led by Professor Jakob Kellner.
I am a first-year Ph.D. student at the Institute of Discrete Mathematics and Geometry, at TU Wien, in Vienna, Austria, under the supervision of Professors Diego A. Mejía and Jakob Kellner. I belong to the research group FB8 Set Theory.
My area of interest focuses on set theory and mathematical logic. Particularly, I am interested in iterated forcing, topology, and philosophy of mathematics.
In my bachelor's thesis, I studied a classical problem in general topology: the normal Moore space conjecture, which states that every normal Moore space is metrizable, and which turned out to be related to strongly compact cardinals. A weak version of the conjecture states that every separable normal Moore space is metrizable. This weak er conjecture is independent in ZFC, and in the thesis, we gave an actual and detailed presentation of this result.
In my master's thesis, I studied forcing iterations using finitely additive measures. This forcing method was defined by Saharon Shelah in 2000 to prove that, consistently, the covering of the null ideal may have countable cofinality. Later, in 2019, Jakob Kellner, Saharon Shelah, and Anda Tanasie made some generalizations, among them, they managed to generalize the notions of forcing to prove an extension theorem at successor steps, however, there remained an open problem: to find conditions for proving a theorem at limit steps. In the thesis, this problem was solved, and this allowed us to present a general theory of iterated forcing using finitely additive measures, in which we can iterate with any μ-FAM-linked forcing notion, a new linkedness property that turned out to be the key to be able to iterate with this type of measures. Concerning applications, we present a new constellation of Cichoń's diagram: a separation of the left-hand side allowing the covering of the null ideal singular, moreover, with countable cofinality.
Danube River, Budapest, December 2023.
Currently, in my first year of Ph.D., I am still interested in forcing theory using finitely additive measures, in particular, I am exploring ways to use these measures on two-dimensional iteration matrices to get new separations of Cichoń's diagram. In addition, I want to investigate the possibility of using this method to force more singular characteristic cardinals. This is a joint work with Miguel A. Cardona and Diego A. Mejía.
Upcoming Activities
May 10, 2024. I will give a talk at the Internal Seminar of the Department of Mathematics at Pavol Jozef Šafárik University, in Košice, Slovakia.
May 24, 2024. I will give a talk at the Colloquium of the Department of Mathematics, at Pontificia Universidad Javeriana, in Bogotá, Colombia. (Online).
May 31-June 2, 2024. I will attend the 2nd Wroclaw Logic Conference in Wroclaw, Poland.
May 31-June 2, 2024. I will present a poster at the 2nd Wroclaw Logic Conference in Wroclaw, Poland.
June 2-June 9, 2024. I will make a research visit at the Mathematical Institute at Wroclaw University, in Wroclaw, Poland, hosted by Professor Piotr Borodulin-Nadziega.
June 4, 2024: I will give a talk at Set Theory Seminar at the Mathematical Institute at Wroclaw University, in Wroclaw, Poland.
June 17-June 21, 2024: I will attend the Young Set Theory Workshop at Erdős Center, in Budapest, Hungary.
October 2024-Fabruary 2025: I will do a 5-month internship at Kobe University, in Kobe, Japan.
Recent Activities
April 22, 2024. I officially started my P.hD. at the Institute of Discrete Mathematics and Geometry, at TU Wien, in Vienna, Austria.
March 21, 2024. I was invited to give a talk at the Colloquium of the Department of Mathematics, at Pontificia Universidad Javeriana, in Bogotá, Colombia. (Online).
March 15, 2024. I gave a talk at the Košice Set Theory & Topology Seminar and at the Internal Seminar of the Department of Mathematics at Pavol Jozef Šafárik University, in Košice, Slovakia.
March 9-March16, 2024. I did a research visit at Pavol Jozef Šafárik University, in Košice, Slovakia.
March 7, 2024. I gave a talk at the Vienna Research Seminar in Set Theory, in the Faculty of Mathematics of the University of Vienna. Abstract. Abstract (ESTS).
February 22, 2024. I received an invitation to give a talk at the Vienna Research Seminar in Set Theory, in the Faculty of Mathematics of the University of Vienna.
February 20, 2024. I received an invitation to make a research visit at the Mathematical Institute at Wroclaw University, in Wroclaw, Poland.
February 13, 2024. I received an invitation to make a research visit at Pavol Jozef Šafárik University in Košice, Slovakia, hosted by Professor Jaroslav Šupina.
January 27–February 3, 2024: I attended the Winter School in Abstract Analysis 2024, section Set Theory & Topology, in Hejnice, Czech Republic.
January 25, 2024. My conference paper The intersection number for forcing notions (to appear in the Proceedings of RIMS Set Theory Workshop 2023) has been posted on arXiv. ResearchGate.
Recent Activities (2023)
December 20, 2023. My paper The measure algebra adding θ-many random reals is θ-FAM-linked (with Diego A. Mejía) has been posted on arXiv. ResearchGate.
November 18, 2023. My paper Which came first, set theory or logic? (with Julián Pulgarín) has been posted on arXiv. ResearchGate.
November 3, 2023. I gave a talk at the Colloquium of the Mathematics school at Universidad Nacional de Colombia titled Multiverses in Mathematics: From the Continuum Hypothesis to the Forcing Theory.
October 24, 2023. I gave a talk at the RIMS Set Theory Workshop: Large Cardinals and the Continuum in Kyoto, Japan, Online, titled A General Theory of Iterated Forcing Theory Using Finitely Additive Measures.
October 20, 2023. I received my master's degree.
October 16, 2023. Research visit at the Universidad Nacional de Colombia, Medellín, Colombia. (Until November 4, 2023).
October 13, 2023. I received an invitation to give a talk at the colloquium of the mathematics school at Universidad Nacional de Colombia, in Medellín, Colombia.
July 12, 2023. I started my job as a project assistant at the Institute of Discrete Mathematics and Geometry, TU Wien, in Vienna, Austria.
June 7, 2023. I officially received the summa cum laude distinction for my master's thesis.
March 8, 2023. I defended my master's thesis: it was approved and a summa cum laude distinction was proposed by the referees.
Contact Information
Email: andres(dot)zapata(at)tuwien(dot)ac(dot)at
Alternative Email: anfuribeza(at)unal(dot)edu(dot)co
Address: Wiedner Hauptstraße 8–10/104 1040 Wien, Austria
Website: auto-self reference.
ResearchGate: https://www.researchgate.net/profile/Andres-Uribe-Zapata-2
