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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 second-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 weaker 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. The first version of this forcing method was introduced 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 introduced the notion of strong-FAM-limit to prove an extension theorem at successor steps, however, there remained an open problem: to find conditions for proving an extension 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.

In May 2025, I was awarded the Shizu and Yu Takeuchi Prize for the Best Master's Thesis in Natural Sciences in Colombia, granted by the Colombian Academy of Exact, Physical and Natural Sciences.

Danube River, Budapest, December 2023.

Currently, in my second 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

October 21-26: I will visit the Department of Mathematics and Statistics at the University of Helsinki, in Helsinki, Finland, hosted by Dr. Miguel Moreno.
September 19, 2025: I will give a talk in the Set Theory Seminar at Tokyo University, in Tokyo, Japan.
September 12: I will give a contributed talk at the 18th Asian Logic Conference (ALC), at Kyoto Sangyo University, in Kyoto, Japan.
September 8-12: I will attend the 18th Asian Logic Conference (ALC) at Kyoto Sangyo University in Kyoto, Japan.
September 4: I will give an invited talk at the Conference on the occasion of Jörg Brendle's 60th birthday, at Kobe University in Kobe.
September 1-5: I will attend the Conference on the occasion of Jörg Brendle's 60th birthday, at Kobe University in Kobe, Japan.
July 30: I will give a talk at the Kobe Set Theory Seminar at Kobe University in Kobe.
July 23 - September 24: I will visit Kobe University, in Kobe, Japan, hosted by Professor Diego A. Mejía.
July 16-18: I will attend the Vienna Oracle of Set Theory at TU Wien, in Vienna, Austria.
July 14-15: I will attend the Conference in honor of Saharon Shelah’s 80th birthday at TU Wien in Vienna, Austria.

Recent Activities (2025)

July 9: My paper Absoluteness of the Riemann Integral (with Carlos M. Parra) was accepted in Journal of Logic and Analysis.
June 28: I was awarded a 2.5-year DOC Fellowship by the Austrian Academy of Sciences (ÖAW).
May 20: I won the Shizu and Yu Takeuchi Prize 2024 for the best thesis in natural sciences in Colombia, awarded by the Colombian Academy of Exact, Physical, and Natural Sciences.
May 16: I gave a talk at the Košice Set Theory & Topology Seminar and the Internal Seminar of the Department of Mathematics at Pavol Jozef Šafárik University, in Košice, Slovakia.
May 11-25: I did a visit at Pavol Jozef Šafárik University in Košice, Slovakia, hosted by Professor Jaroslav Šupina.
March 19, 2025: My paper The Measure Algebra Adding θ-Many Random Reals is θ-FAM-Linked (with Diego A. Mejía) has been published in Topology and its Applications. DOI.
March 11, 2025. My paper Finitely Additive Measures on Boolean Algebras (with Diego A. Mejía and Miguel A. Cardona) has been posted on ResearchGate. arXiv.
September 30, 2024-March 1, 2025: I did an internship at Kobe University, in Kobe, Japan, hosted by Professors Diego Mejía and Joerg Brendle.
January 28, 2025. My paper Absoluteness of the Riemann Integral (with Carlos M. Parra-Londoño) has been posted on ResearchGate. arXiv.
January 14, 2025. My paper Probability Trees (with Diego A. Mejía) has been posted on arXiv. ResearchGate.

Recent Activities (2024)

December 23, 2024: I gave a talk at the 19th Kansai Set Theory seminar at Osaka Metropolitan University, in Osaka, Japan.
December 23 - December 24, 2024: I attended the 19th Kansai Set Theory seminar at Osaka Metropolitan University, in Osaka, Japan.
December 18, 2024: I gave a talk at the Shizuoka Set Theory Seminar, at Shizuoka University, Japan.
December 17 - December 21, 2024: I visited Shizuoka University, in Shizuoka, Japan.
November 20, 2024: I gave a talk at the Kobe Set Theory Seminar, at Kobe University, Japan.
November 13, 2024: I gave a talk at the Kobe Set Theory Seminar, at Kobe University, Japan.
October 9-October 11, 2024: I attended the RIMS Set Theory Workshop 2024, in Kyoto, Japan.
October 9, 2024: I gave a talk at the RIMS Set Theory Workshop 2024, in Kyoto, Japan. Slides.
October 1, 2024: My paper The measure algebra adding θ-many random reals is θ-FAM-linked (with Diego A. Mejía) was accepted in Topology and its Applications.
September 16-September 20: I attended the European Set Theory Conference 2024, in Münster, Germany.
September 19: I gave a talk at the European Set Theory Conference 2024, in Münster, Germany.
July 26, 2024. I gave a talk at the Colloquium of the Department of Mathematics, at Pontificia Universidad Javeriana, in Bogotá, Colombia. (Online).
July 8-July 12, 2024: I attended the conference 120 Years of Choice at Leeds University, in Leeds, United Kingdom.
July 11, 2024. I presented a poster at the conference 120 Years of Choice at Leeds University, in Leeds, United Kingdom.
June 24-June 28, 2024: I attended the workshop Determinacy, Inner Models and Forcing Axioms at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI), in Vienna, Austria.
June 17-June 21, 2024: I attended the Young Set Theory Workshop at Erdős Center, in Budapest, Hungary.
June 20, 2024: I presented a poster at the Young Set Theory Workshop at Erdős Center, in Budapest, Hungary.
June 14, 2024. My paper A general theory of iterated forcing using finitely additive measures (with Diego A. Mejía and Miguel Cardona) has been posted on arXiv. ResearchGate.
June 3-June 9, 2024. I made 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 2, 2024. I presented a poster at the 2nd Wroclaw Logic Conference in Wroclaw, Poland.
May 30-June 2, 2024. I attended the 2nd Wroclaw Logic Conference in Wroclaw, Poland.
May 10, 2024. I gave a talk at the Internal Seminar of the Department of Mathematics at Pavol Jozef Šafárik University, in Košice, Slovakia.
April 22, 2024. I officially started my P.hD. at the Institute of Discrete Mathematics and Geometry, at TU Wien, in Vienna, Austria.
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).
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

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