논문 (2011 - )
'Amalgamation functors and boundary properties in simple theories' (with J. Goodrick and A. Kolesnikov), Israel Journal of Math., 193 (2013) 169-207.
'Amalgamation functors and homology groups in model theory' (with J. Goodrick and A. Kolesnikov), in Proceedings of ICM 2014, Volume II (2014) 41-58.
'Homology groups of types in model theory and the computation of H2(p)' (with J. Goodrick and A. Kolesnikov), J. of Symbolic Logic, 78 (2013) 1086-1114.
'Notions around tree property 1' (with H-J. Kim), Annals of Pure and Applied Logic, 162 (2011) 698-709. Erratum: Kim-independence in each example of Example 0.1 satisfies all the basic axioms and type-amalgamation of Lascar types, except base monotonicity. See the paper below "Independence over arbitrary sets in NSOP1 theories."
'Tree indiscernibilities, revisited' (with H-J. Kim and L. Scow), Archive for Math. Logic, 53 (2014) 211-232.
'The Lascar group, and the strong types of hyperimaginaries', Notre Dame Journal of Formal Logic, 54 (2013) 497-507.
'Characterization of the second homology group of a stationary type in a stable theory' (with J. Goodrick and A. Kolesnikov), in Proceedings of the 13th Asian Logic Conference, World Scientific, (2015) 93-104.
'A classification of 2-chains having 1-shell boundaries in rosy theories' (with SunYoung Kim and Junguk Lee), J. of Symbolic Logic, 80 (2015) 322-340. Erratum - The fixed strong type p should be a type of an algebraically closed tuple (over its parameter), since each vertex of simplices in p are defined to be an algebraically closed set.
'Type-amalgamation properties and polygroupoids in stable theories' (with J. Goodrick and A. Kolesnikov), J. of Math. Logic, 15 (2015) 45 pp.
'Homology groups of types in stable theories and the Hurewicz correspondence' (with J. Goodrick and A. Kolesnikov), Annals of Pure and Applied Logic, 168 (2017) 1710-1728.
'On the n-uniqueness of types in rosy theories', Archive for Math Logic, 55 (2016) 677-686.
'The Lascar groups and the first homology groups in model theory' (with J. Dobrowolski and J. Lee), Annals of Pure and Applied Logic, 168 (2017) 2129-2151.
'The relativized Lascar groups, type-amalgamation, and algebraicity' (with J. Dobrowolski, A. Kolesnikov, and J. Lee), J. of Symbolic Logic, 86 (2021) 531-557.
'Independence over arbitrary sets in NSOP1 theories' (with J. Dobrowolski and N. Ramsey), APAL, 173 (2022) 103058.
'On the number of countable models of a countable NSOP1 theory without weight ω' J. of Symbolic Logic, 84 (2019) 1168-1175.
'Non-commutative groupoids obtained from the failure of 3-uniqueness in stable theories' (with S. Kim and J. Lee), Fundamenta Mathematicae, 249 (2020) 47-70.
'More on tree properties' (with E. Casanovas), Fundamenta Mathematicae, 249 (2020) 287-301.
'Transitivity, lowness, and ranks in NSOP1 theories' (with A. Chernikov and N. Ramsey), submitted. We study consequences of transitivity of Kim-independence over sets in NSOP1 theories. In particular we show that Lascar types are strong types in low NSOP1 theories with nonforking existence, extending S. Buechler's result on low simple theories.
'Weak canonical bases in NSOP1 theories' J. of Symbolic Logic, 86 (2021) 1259-1281.
'Automorphism groups over a hyperimaginary' (with H. Lee), J. of Math. Soc. of Japan 75 (2023) 21-49.
'Existence in NSOP1 theories' (with J. Kim and H. Lee), in preparation. We show that Kim-forking satisfies existence in all NSOP1 theories.
강연 파일
A talk presented at BIRS, Canada, Feb. 2009.
Talk slides (revised): Recent development of model theory, Oleron, France, June 2011.
A talk presented at 16th Asian Logic Conference, Kazakhstan, June 2019.
Colloquium 강연, KIAS, May 2022.
강의록
저술
한글 원고 (hwp 파일은 내려받아 보세요.)
올바른 수학을 찾아서 (2003)
괴델과 그의 불완전성 정리, (네이버캐스트) (2006)
앨런튜링 탄생 100주년을 기념하며 (2012)
P 대 NP (2016)
집합론, 강제법, 가상과 실제의 대화 (2017)
칸토어와 집합론 (2018)
수리논리 학술회의 및 강연회
왜 괴델인가? (강연록): 괴델탄생 백주년 기념 학술대회, 2006년 4월 15일, 연세대학교.
2009 수리논리 여름학교: 집합론, 다이아몬드를 찾아서, 6월 18-22일, 대전 스파피아 호텔.
2010 Spring Model Theory School, 5월 16-18일, 연세대학교
2010 Model Theory Conference, 5월 19-22일, 연세대학교
튜링탄생 100주년 기념 강연회 및 계산이론 여름학교 2012, 6월 23-26일, 대전
Classification Theory Workshop, 2014년 8월 6-9일, 대전
Isaac Goldbring 교수 zoom 강연 시리즈: The Connes Embedding Problem, MIP*=RE, and Model Theory, 2022년 1월 4일 ~ 2월 22일 매주 수요일 11시~12:20분(한국시간)