Mailing Address:

Department of Mathematics

Yonsei University

50 Yonsei-ro, Seodaemun-gu

Seoul 03722, South Korea

Telephone: (02) 2123-2585

Fax: (02) 392-6634

E-mail: bkim(at)yonsei.ac.kr

I am a Professor of Mathematics at Yonsei University.

# Papers (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), J. of Symbolic Logic, 88 (2023) 919-946. 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. We also supply a revised argument to construct Morley trees.

'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), submitted. We show that Kim-forking satisfies existence in all NSOP1 theories.

# Slides

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.

# Lecture Notes

A course lecture on basic Set Theory.

A course lecture on basic Mathematical Logic.

A course lecture on Gödel's Incompleteness Theorems.

# Books

# Meetings/Lectures on Mathematical Logic in Korea

Logic Summer School; Set Theory, a passage to the diamond, Spapia Hotel, Daejeon, Korea, June 18-22, 2009.

2010 Spring Model Theory School, May 16-18, Yonsei Univ., Seoul, Korea

2010 Model Theory Conference, May 19-22, Yonsei Univ., Seoul, Korea

Turing Centenary and Theory of Computation Summer School, Daejeon, Korea, June 23-26, 2012

Classification Theory Workshop, Daejeon, Korea, August 6-9, 2014

The 15th Asian Logic Conference, Daejeon, Korea, July 10-14, 2017

Isaac Goldbring's zoom lecture series: The Connes Embedding Problem, MIP*=RE, and Model Theory, Wednesdays in January 4 - February 22, 2022

Model Theory Conference in Seoul, Yonsei University, August 28-30, 2023