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ON WEAK INDEPENDENCE THEOREM (Model theoretic aspects of the notion of independence and dimension)

HOFFMANN, DANIEL MAX 京都大学

2023.04

概要

This text is based on my talk at the RIMS Model Theory Workshop, taking place
in December 2022. In October 2022, [3] was accepted for publication in the Journal
of Mathematical Logic and it is a quite long paper achieving various results, some
of them being technical and so difficult to read separately. My talk at the RIMS
was thought as a transparent exposition of one of the main results from [3], which
is of a more geometric flavor and so easier to extract from the whole text.
I thank organizers of the RIMS Model Theory Workshop 2022. Moreover, I take
- again - the opportunity to express my gratitude to Hirotaka Kikyo for his support
and enormous kindness. ...

参考文献

[1] G. Cherlin, L. van den Dries, and A. Macintyre. The elementary theory of regularly closed

fields. Available on http: //sites.math.rutgers. eduJ-cherlin/Preprint/CDM2 .pdf.

[2] Jan Dobrowolski, Daniel Max Hoffmann, and Junguk Lee. Elementary equivalence theorem

for pac structures. The Journal of Symbolic Logic, 85(4):1467-1498, 2020.

[3] Daniel Max Hoffmann and Junguk Lee. Co-theory of sorted profinite groups for pac structures.

Journal of Mathematical Logic, 0(0):2250030, 0.

[4] Itay Kaplan and Nicholas Ramsey. On Kim-independence. Journal of the European Mathematical Society, 22:1423 - 1474, 2020.

[5] Byunghan Kim and Anand Pillay. Simple theories. Annals of Pure and Applied Logic, 88(23):149-164, 1997. Joint AILA-KGS Model Theory Meeting.

lNSTITUT FUR GEOMETRIE, TECHNISCHE UNIVERSITAT DRESDEN, DRESDEN, GERMANY

and

lNSTYTUT MATEMATYKI, UNIWERSYTET WARSZAWSKI, WARSZAWA, POLAND

E-mail address: daniel. max. hoffmann©gmail. com

URL: https://sites.google.com/site/danielmaxhoffmann/

...

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