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MEJIA Guzman Alejandro DiegoGraduate School of System Informatics / Department of System InformaticsAssociate Professor
Researcher basic information
■ Research Keyword- Boolean algebras
- Forcing theory
- Ideals on the natural numbers
- Ultrafilters on the natural numbers
- Cichon's diagram
- Forcing iterations
- Cardinal characteristics of the continuum
■ Committee History
- Apr. 2026 - Jun. 2026, RPTU University Kaiserslautern-Landau, External Examiner for PhD Thesis
- Jul. 2025 - Aug. 2025, FWF (Austrian Science Fund), Evaluator
- Jan. 2025 - Feb. 2025, United States - Israel Binational Science Foundation (BSF), Project referee
- Oct. 2023 - Jan. 2025, Banff International Research Station, Project referee
- Mar. 2023 - Mar. 2023, Israel Science Foundation, Project referee
Research activity information
■ Award- Oct. 2025 National University of Colombia (Medellín Campus), Faculty of Sciences, Recognition Motion, Outstanding Contribution as a Graduate of the Master’s Program in Mathematical SciencesCurrently an Associate Professor at Kobe University, recognized as one of the leading researchers in set theory worldwide. His academic work and continuous support for young Colombian mathematicians demonstrate a strong commitment to the advancement of knowledge and to the international projection of the Colombian scientific community.Others
- Oct. 2025 Alejandro Ángel Escobar Foundation, Honorable Mention: 2025 National Awards for Science and Solidarity, Iterated Forcing with Finitely Additive Measures: Applications of Probability to Forcing TheoryInternational academic award
- May 2025 Colombian Academy of Exact, Physical, and Natural Sciences, Shizu and Yu Takeuchi prize 2024 for the Best Master Thesis (advisor), Iterated forcing with finitely additive measures: applications of probability to forcing theoryInternational society
- Apr. 2022 Shizuoka University, 第5期静岡大学若手重点研究者の称号Others
- Apr. 2010 MEXT (Japan), Japanese Government (MEXT) Scholarship, Scholarship for doctoral studiesInternational academic award
- Jan. 2007 Mazda Foundation for Arts and Sciences, Mazda fellowship from the Mazda Foundation for Arts and Sciences, Scholarship for master studiesPublisher
- Sep. 2006 Universidad de Antioquia, Best university degree by program, Best university degree by programInternational academic award
- Sep. 2004 Universidad de Antioquia, Worth exaltation in the Scientific Field for distinguised participation at the Colombian Mathematical Olympiad, Worth exaltation in the Scientific Field for distinguised participation at the Colombian Mathematical OlympiadInternational academic award
- Dec. 2003 Universidad Antonio Narino, Bronze medal, VII Colombian Mathematical Olympiad, Bronze medal, VII Colombian Mathematical OlympiadJapan society
- Dec. 2003 Universidad Antonio Narino, Silver Medal, VI Iberoamerican Mathematical Olympiad, Silver Medal, VI Iberoamerican Mathematical OlympiadInternational society
- Mar. 2001 Universidad de Antioquia, Honor scholarship (Dean's list), Honor scholarship (Dean's list)International academic award
- Corresponding, Mar. 2026, Comptes Rendus. Mathématique, 364, 107 - 125, English, International magazine, Co-authored internationally[Refereed]Scientific journal
- Corresponding, Dec. 2025, Dissertationes Mathematicae, 607, 1 - 67, English, International magazine[Refereed]Scientific journal
- Corresponding, Aug. 2025, The Journal of Symbolic Logic, English[Refereed]Scientific journal
- Corresponding, World Scientific Pub Co Pte Ltd, Apr. 2025, Journal of Mathematical Logic, English[Refereed]Scientific journal
- Corresponding, Apr. 2025, Annals of Pure and Applied Logic, 176(4) (4), 103537, English[Refereed]Scientific journal
- Elsevier BV, Mar. 2025, Topology and its Applications, 371(1) (1), 109371, English[Refereed][Invited]Scientific journal
- Dec. 2024, Boletin de Matematicas, 31(1) (1), 1 - 48, English[Refereed]Scientific journal
- Corresponding, Elsevier BV, Jul. 2024, Annals of Pure and Applied Logic, 175(7) (7), 103453, English[Refereed]Scientific journal
- Corresponding, Jun. 2024, Boletin de Matematicas (Universidad Nacional de Colombia), 30(2) (2), 61 - 80, Spanish, Castilian, Co-authored internationally[Refereed][Invited]International conference proceedings
- Abstract We propose a reformulation of the ideal $\mathcal {N}$ of Lebesgue measure zero sets of reals modulo an ideal J on $\omega $ , which we denote by $\mathcal {N}_J$ . In the same way, we reformulate the ideal $\mathcal {E}$ generated by $F_\sigma $ measure zero sets of reals modulo J, which we denote by $\mathcal {N}^*_J$ . We show that these are $\sigma $ -ideals and that $\mathcal {N}_J=\mathcal {N}$ iff J has the Baire property, which in turn is equivalent to $\mathcal {N}^*_J=\mathcal {E}$ . Moreover, we prove that $\mathcal {N}_J$ does not contain co-meager sets and $\mathcal {N}^*_J$ contains non-meager sets when J does not have the Baire property. We also prove a deep connection between these ideals modulo J and the notion of nearly coherence of filters (or ideals). We also study the cardinal characteristics associated with $\mathcal {N}_J$ and $\mathcal {N}^*_J$ . We show their position with respect to Cichoń’s diagram and prove consistency results in connection with other very classical cardinal characteristics of the continuum, leaving just very few open questions. To achieve this, we discovered a new characterization of $\mathrm {add}(\mathcal {N})$ and $\mathrm {cof}(\mathcal {N})$ . We also show that, in Cohen model, we can obtain many different values to the cardinal characteristics associated with our new ideals.Corresponding, Cambridge University Press (CUP), Dec. 2023, The Journal of Symbolic Logic, 90(3) (3), 1098 - 1128, English[Refereed]Scientific journal
- Jul. 2022, Archive for Mathematical Logic, 61, 653 - 683[Refereed]Scientific journal
- Jul. 2022, Archive for Mathematical Logic, 61, 599 - 610[Refereed]Scientific journal
- Institute of Mathematics, Polish Academy of Sciences, May 2022, Colloquium Mathematicum, 170(1) (1), 115 - 144, English[Refereed]Scientific journal
- Universidad Industrial de Santander, Mar. 2022, Revista Integración, 40(1) (1), 1 - 23[Refereed]Scientific journal
- European Mathematical Society - {EMS} - Publishing House {GmbH}, Nov. 2021, Journal of the European Mathematical Society, 24(11) (11), 3951 - 3967, English[Refereed]Scientific journal
- Nov. 2021, Israel Journal of Mathematics, 246(1) (1), 73 - 129[Refereed]Scientific journal
- Jan. 2021, Annals of Pure and Applied Logic, 172(1) (1), 102856[Refereed]Scientific journal
- 2021, Journal of Mathematical Logic, 21(3) (3), 2150018[Refereed]Scientific journal
- Mathematical Society of Japan (Project Euclid), Apr. 2020, Journal of the Mathematical Society of Japan, 72(2) (2), 413 - 433[Refereed]Scientific journal
- Sep. 2019, Mathematical Logic Quarterly, 65(2) (2), 170 - 199[Refereed]Scientific journal
- Feb. 2019, Revista Colombiana de Matematicas, 53(2) (2), 109 - 123[Refereed]Scientific journal
- {WORLD} {SCIENTIFIC}, Jan. 2019, Proceedings of the 14th and 15th Asian Logic Conferences, 213 - 248, English[Refereed][Invited]International conference proceedings
- Cambridge University Press, Mar. 2018, Journal of Symbolic Logic, 83(1) (1), 208 - 236, English[Refereed]Scientific journal
- Jun. 2017, CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 69(3) (3), 502 - 531, English[Refereed]Scientific journal
- Apr. 2016, Proceedings of the American Mathematical Society, 144(9) (9), 4025 - 4042[Refereed]Scientific journal
- Nov. 2015, ANNALS OF PURE AND APPLIED LOGIC, 166(11) (11), 1071 - 1109, English[Refereed]Scientific journal
- 2014, FUNDAMENTA MATHEMATICAE, 227(1) (1), 35 - 68, English[Refereed]Scientific journal
- May 2013, ARCHIVE FOR MATHEMATICAL LOGIC, 52(3-4) (3-4), 261 - 278, English[Refereed]Scientific journal
- Corresponding, Universidad Industrial de Santander, Dec. 2011, Revista Integracion, 29(2) (2), 143 - 150, Spanish, Castilian, International magazine[Refereed]Scientific journal
- Lead, Kyoto University, Jul. 2026, RIMS Kokyuroku, 2349, 45 - 51, English, Domestic magazineIntroduction international proceedings
- Corresponding, Jul. 2024, 京都大学数理解析研究所講究録, 2290, 43 - 61, EnglishAnatomy of ESummary international conference
- Jul. 2023, Kyoto University RIMS Koukyuuroku, 2261, 47 - 77Localization and anti-localization cardinals
- Apr. 2022, Kyoto University RIMS Koukyuuroku, 2213, 14 - 47
- Jul. 2020, Kyoto University RIMS Koukyuuroku, 2164, 34 - 49
- Mar. 2019, Kyoto University RIMS Koukyuuroku, 2141, 1 - 15
- Aug. 2018, Kyoto University RIMS Koukyuuroku, 2081, 7 - 27
- Oct. 2017, Kyoto University RIMS Koukyuuroku, 2050, 153 - 161
- Jul. 2017, Kyoto University RIMS Koukyuuroku, 2042, 75 - 87
- Kyoto University, May 2015, Kyoto University RIMS Koukyuuroku, 1949, 54 - 61, EnglishBorel computation of names in template iterations.
- Kyoto University, May 2014, Kyoto University RIMS Koukyuuroku, 1895, 68 - 78, EnglishPreservation properties for iterations with finite support
- Kyoto University, Sep. 2013, Kyoto University RIMS Koukyuuroku, 1821, 36 - 48, EnglishModels of some cardinal invariants with large continuum
- Contributor, Finitely Aditive Measures on Boolean Algebras, Springer Proceedings in Mathematics & Statistics, May 2026, English, Accepted Book Chapter[Refereed]Scholarly book
- Editor, Editor, Kyoto University Research Institute for Mathematical Sciences, Sep. 2021, 1-86
- Contributor, Matrix iterations with vertical support restrictions, World Scientific Publications, Jan. 2019, 213-248
- Yamaguchi Set Theory Seminar 2026, Jun. 2026, English, Iwakuni city, Yamaguchi-ken, Japan, Domestic conference, Co-authored internationallyKnaster-like properties at singular cardinalsOral presentation
- Coloquio de Matematicas Oswaldo Dede Mejia, Apr. 2026, Spanish, Castilian, Diego A Mejía.jpg, Others, Flyer, No password, Universidad del Atlantico, Barranquilla, ColombiaThe structure of the real line[Invited]Invited oral presentation
- RIMS Workshop on Set Theory 2025: Recent Developments in Axiomatic Set Theory, Dec. 2025, English, Kyoto University RIMS, Japan, International conference, Co-authored internationallyIsomorphism Theorems for ideals in Polish spacesOral presentation
- 18th Asian Logic Conference, Sep. 2025, EnglishCardinal characteristics of the null-additive and meager-additive idealsOral presentation
- Conference on the occasion of Jörg Brendle's 60th birthday, Sep. 2025, EnglishForcing techniques for finite support iterationsOral presentation
- The Vienna Oracle of Set Theory, Jul. 2025, EnglishThe cofinality of the strong measure zero idealOral presentation
- Logic Colloquium 2025, Jul. 2025, EnglishDirected schemes of ideals and cardinal characteristicsOral presentation
- 19th Kansai Set Theory seminar, Dec. 2024, EnglishStrong measure zero, additive ideals, and their cardinal characteristicsOral presentation
- Symposium on Advances in Mathematical Logic, Jul. 2024, JapaneseSlalom numbers[Invited]Invited oral presentation
- Shizuoka University, Special Seminar in Set Theory, Mar. 2024, EnglishMalliaris' and Shelah's p=t (mini-course)[Invited]Public discourse
- University of Vienna, Research Seminar in Set Theory, EnglishMini-course: Forcing techniques for Cichon's Maximum[Invited]Public discourse
- Wroclaw Set Theory Seminar, Nov. 2023, EnglishUltrafilters and finitely additive measures in forcing theory[Invited]Public discourse
- Logic Colloquium, University of Vienna, Nov. 2023, EnglishIterations with ultrafilter-limits and fam-limits[Invited]Public discourse
- 京都大学RIMS研究集会2023巨大基数と連続体, Oct. 2023, Domestic conferenceTwo-dimensional iterations with fam-limits
- 56th National Congress of the Mexican Mathematical Society, Oct. 2023, Domestic conferenceJapan and the real numbers (in Spanish)[Invited]
- Iberoamerican and Pan Pacific International Conference on Topology and its Applications, Sep. 2023, Domestic conferenceFinitely additive measures and closed measure zero sets[Invited]
- University of Vienna, Research Seminar in Set Theory, Jun. 2023, Domestic conferencePreservation results related to finitely additive measures on Boolean algebras[Invited]
- TUKE x UPJS Colloquium, Jun. 2023, Domestic conferenceForcing and combinatoris of the reals[Invited]
- Colombia-Mexico seminar of Set Theory, Nov. 2022, Domestic conferenceCofinality of the ideal of strong measure zero sets[Invited]
- 京都大学RIMS研究集会2022強制法と基数算術の新たな展開, Oct. 2022, Domestic conferenceMeasure zero modulo ideals
- 日本数学会2022年度秋季総合分科会, Sep. 2022, Domestic conference強測度ゼロ集合のイデアルに関連する基数不変量
- ESI Set Theory Workshop, Jul. 2022, Domestic conferenceCardinal Characteristics Associated with the Ideal of Strong Measure Zero Sets[Invited]
- 1st Meeting Brazil-Colombia in Logic, Dec. 2021, Domestic conferenceVariations of the negation of Riis’ axiom[Invited]
- XI Simposio Nororiental de Matematicas, Dec. 2021, Domestic conferenceMeasure zero modulo ideals[Invited]
- II Workshop of Basic Sciences: a closeup to Engineering applications, Oct. 2021, Domestic conferenceThe infinite and the real numbers[Invited]
- RIMS研究集会2021 実数の集合論における近年の進展, Oct. 2021, Domestic conferenceRecent forcing techniques: restrictions to submodels I and II[Invited]
- Science Mondays, Sep. 2021, Domestic conferenceCombinatorics of the real line since its beginnings[Invited]
- XVI International Luminy Workshop in Set Theory, Sep. 2021, Domestic conferenceContinuum-many many things[Invited]
- A short talk series: Research in Set Theory, Jun. 2021, Domestic conferenceCoherent systems of finite support iterations[Invited]
- Kobe Set Theory Workshop 2021 on the occasion of Sakaé Fuchino's Retirement, Mar. 2021, Domestic conferencePreserving failures of simple fragments of Martin's axiom[Invited]
- 日本数学会2020年度秋季総合分科会, Sep. 2020, Domestic conferenceLebesgue measure zero modulo ideals
- Research Seminar, Kurt Goedel Research Center, University of Vienna, May 2020, Domestic conferencePreserving splitting families[Invited]
- XVIII Latin American Symposium of Mathematical Logic, Dec. 2019, Domestic conferenceCichon's maximum without large cardinals[Invited]
- 京都大学RIMS研究集会2019集合論と無限, Nov. 2019, Domestic conferenceCichon's maximum without large cardinals
- 日本数学会2019年度秋季総合分科会, Sep. 2019, Domestic conferenceCichon's maximum over ZFC alone[Invited]
- Set Theory of the Reals, Aug. 2019, Domestic conferencePreservation Theorems of finite support iterations I and II[Invited]
- RIMS研究集会2018 公理的集合論とその応用, Nov. 2018, Domestic conferenceMany different uniformity numbers of Yorioka ideals
- Set Theory Today: A conference in honor of Georg Cantor, Sep. 2018, Domestic conferenceFilter-linkedness and its effect on cardinal characteristics of the continuum[Invited]
- Joint meeting of the Colombian and Mexican Mathematical Society, May 2018, Domestic conferenceFilter-linkedness and its effect on cardinal characteristics of the continuum[Invited]
- 日本数学会2018年度年会, Mar. 2018, Domestic conference強制法理論及び連続体上の組合せ論
- 2nd Pan Pacific International Conference on Topology and Applications, Nov. 2017, Domestic conferenceUltrafilter limits in matrix iterations[Invited]
- RIMS研究集会2017 反復強制法の理論と基数不変量, Nov. 2017, Domestic conferenceRecent (and not that recent) forcing techniques on finite support iterations[Invited]
- The 15th Asian Logic Conference, Jul. 2017, Domestic conferenceMultiple dimensional finite support iterations[Invited]
- RIMS研究集会2016 無限組合せ論と強制法理論, Nov. 2016, Domestic conferenceThe left side of Cichon's diagram
- RIMS研究集会2016 数学基礎論とその応用, Sep. 2016, Domestic conferenceSeveral Values in Cichon's diagram
- Winter School in Abstract Analysis, section: Set Theory and Topology, Feb. 2016, Domestic conferenceExpected values for the a.d. number and 3D-iterations
- 1st Pan Pacific International Conference on Topology and Applications, Nov. 2015, Domestic conferenceCardinal invariants of ideas related to the strong measure zero ideal[Invited]
- The 19th Midrasha Mathematicae, 8th Young Set Theory Workshop, Oct. 2015, Domestic conferenceMany different values in Cichon's diagram[Invited]
- Winter School in Abstract Analysis, section: Set Theory and Topology, Feb. 2015, Domestic conferenceSplitting, bounding and almost disjointness number
- Workshop on Mathematical Logic on the Occasion of Sakae Fuchino's 60th Birthday, Nov. 2014, Domestic conferenceCichon's diagram and large continuum[Invited]
- RIMS研究集会2014 集合論における無限組み合わせ論とその応用, Nov. 2014, Domestic conferencesba
- Logic Colloquium 2014, Jul. 2014, Domestic conferenceMatrix iterations and Cichon's diagram[Invited]
- ESI Set Theory Programme. Forcing and large cardinals workshop, Sep. 2013, Domestic conferenceRothberger gaps in F_\sigma ideals[Invited]
- RIMS研究集会2013 反映原理と巨大基数の集合論, Sep. 2013, Domestic conferenceTemplate iterations with non-definable posets
- RIMS研究集会2012 強制法による拡大と巨大基数, Dec. 2012, Domestic conferenceModels of some cardinal invariants with large continuum
- Joint FWF-JSPS Seminar on Forcing in Set Theory, Jan. 2012, Domestic conferenceMatrix iterations and Cichon's diagram[Invited]
- 数学基礎論若手の会 2011, Dec. 2011, Domestic conferenceForcing iterations and Cichon's diagram
- European Set Theory SocietyApr. 2025 - Present
- Colombian Mathematical SocietyJan. 2018 - Present
- The Mathematical Society of JapanOct. 2017 - Present
- Association for Symbolic LogicApr. 2010 - Present
■ Research Themes
- 基盤研究(C), Apr. 2023 - Mar. 2027Advances on Combinatorics of the real line and topology
- 若手研究(B), 若手研究(B), Apr. 2018 - Mar. 2022反復強制法の理論における新たな発展Competitive research funding
- Others, 高校生の受け入れ, 01 Aug. 2024 - 30 Jun. 2025静岡大学FSS
- Lecturer, 18 Sep. 2024 - 18 Sep. 2024コロンビア国立大学での講義(オンライン)
- Others, 07 Aug. 2024 - 08 Aug. 2024静岡大学私立高校SSH
- Others, 高校生の受け入れ, 01 Oct. 2023 - 15 Jun. 2024静岡大学FSS
- Other than myself, University of Antioquia website, Nov. 2025Internet
- National University of Colombia Agency, 03 Oct. 2025, Medellin (Colombia)Internet
- La Patria (newspaper), 28 Sep. 2025, ColombiaPaper
- UN Radio (Colombia), UNAL News, 28 May 2025, Medellin (Colombia), Interview to Andres Uribe-Zapata and his thesis advisors Diego A. Mejia and Carlos M. Parra, about his Prize Shizu and Yu Takeuchi 2024 for the best Master Thesis, awarded by the Colombian Academy of ScienceMedia report
- Program Committee (Set Theory), XXI SLALM01 Jun. 2026 - 05 Jun. 2026, Bogota, ColombiaCompetition etc
- Scientific Committee, The 10th European Set Theory Conference18 May 2026 - 22 May 2026, Helsinki, FinlandAcademic society etc
- Organizer, Conference on the occasion of Jörg Brendle's 60th birthday02 Sep. 2025 - 05 Sep. 2025Academic society etc
- Program Committee, XXIV Colombian Congress of Mathematics02 Jun. 2025 - 06 Jun. 2025Academic society etc
- Organizer, Young Logicians Gathering in Japan 202225 Nov. 2022 - 27 Nov. 2022Academic society etc
- Organizer, Kyoto University RIMS Workshop 2020, Set Theory: Reals and Topology16 Nov. 2020 - 20 Nov. 2020Academic society etc
