@archernikov

Michael Brin professor of mathematics at @UofMaryland. Mathematical logic, model theory -and connections to combinatorics, algebra, etc.

 Washington, DC
chernikov.umd.edu/
Joined December 2007
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Saharon Shelah and number 4, a thread. Shelah is an incredibly prolific mathematician working mostly in mathematical logic who has (co-)authored around 1500 papers so far. His other superpower is the ability to discover number 4 where it has absolutely no reason to be. 1/32
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A significant potential resolution of the infinitary form of of one of the oldest problems in mathematical logic, with an interesting background story!
Cameron Freer@cameronfreerOct 11
A counterexample to Vaught’s conjecture for infinitary logic has been verified in Lean! In joint work with Nate Ackerman and Robin Knight, we developed and formalized a construction based on Knight’s unpublished manuscript.
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Some results from the Open AI slopacalypse of interest to mathematical logicians:
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Shelah’s eventual categoricity conjecture for AEC's holds github.com/openai/math/blob/… but not starting with the expected bound github.com/openai/math/blob/… The Partition Principle does not imply Choice github.com/openai/math/blob/…
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The abelian Zilber–Pink conjecture over Q bar github.com/openai/math/blob/… Every finite coloring of the positive integers contains sets of any prescribed finite size whose nonempty subset sums and nonempty subset products all have one common color github.com/openai/math/blob/…

math/preprints/The-Abelian-Zilber-Pink-Conjecture-September-24-2026/paper.pdf at main · openai/math

Contribute to openai/math development by creating an account on GitHub.

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"SOP2=SOP3", arxiv.org/abs/2608.13291 This surprisingly short argument answers an old question of Džamonja and Shelah from 2004, and seems to be the first significant AI-assisted advance in mathematical logic. It is also a result we were lucky not to have found back in the day.

SOP$_2$=SOP$_3$

The classes of SOP$_2$ and SOP$_3$ first-order theories coincide. This answers a question of Džamonja and Shelah from 2004.

arxiv.org
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In view of the recent mathematical developments around famous old conjectures, I would like to share a blogpost by Igor Pak: "What if they are all wrong?" igorpak.wordpress.com/2020/1…

What if they are all wrong?

Conjectures are a staple of mathematics. They are everywhere, permeating every area, subarea and subsubarea. They are diverse enough to avoid a single general adjective. They come in al shapes and …

igorpak.wordpress.com
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Artem Chernikov retweeted
Richard Elwes@RichardElwesApr 9
My book Huge Numbers is out today (in UK) with @BasicBooksUK ! Ian Stewart says: "This fascinating exploration of the giants of the mathematical world is clear, informative, and immensely readable. Wonderful!” 1/2 sciencenews.org/article/huge…

Huge Numbers tackles mathematics at its most incomprehensibly large

Mathematician Richard Elwes surveys googology, the study of enormous numbers, in a new book.

sciencenews.org
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Tom Gur@TomGurFeb 25
Postdoc position in Cambridge with Julia Wolf: Julia is a phenomenal researcher and a wonderful collaborator. She is advertising a 2-year postdoc at the interface of additive combinatorics and model theory. Closing date: 16 March. Details: jobs.ac.uk/job/DQP803/postdo…
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Cameron Freer@cameronfreerJan 20
I'm excited to share de Finetti's theorem formalized in Lean: three different proofs that infinite exchangeable sequences are conditionally IID. 43k lines across 113 files with 600+ lemmas. 💻 code: github.com/cameronfreer/exch… 📊 blueprint: cameronfreer.github.io/excha… (1/3)
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Ken Ono
@KenOno691Jan 23
1/ ANNOUNCING 🎬 MARYAM: The Mirror and the Map, a feature film about Fields Medalist Maryam Mirzakhani (the first woman to win the Fields Medal). After The Man Who Knew Infinity, writer/director Matt Brown, Manjul Bhargava & I are reuniting as associate producers.
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Maryam Mirzakhani's loss is still deeply felt in the math community. It was a beautiful moment for me to see her receive the Fields medal in Seoul in 2014. It's only later that I learned her inspiring story. Really happy that Ken and the team are bringing it to the big screen!
Ken Ono
@KenOno691Jan 23
1/ ANNOUNCING 🎬 MARYAM: The Mirror and the Map, a feature film about Fields Medalist Maryam Mirzakhani (the first woman to win the Fields Medal). After The Man Who Knew Infinity, writer/director Matt Brown, Manjul Bhargava & I are reuniting as associate producers.
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David Chiang@davidweichiang30 Oct 2025
I am recruiting a PhD student to work with me, Peter Cholak, Anand Pillay, and Andy Yang @pentagonalize on transformers and logic/model theory (or related topics). If you are interested, please email me with "FLaNN" in the subject line!
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18th Asian Logic Conference September 8 - 12, 2025 Kyoto Sangyo University, Kyoto, Japan www2.kobe-u.ac.jp/~brendle/a… Plenary Speakers: Artem Chernikov, Su Gao, Fenrong Liu, Takako Nemoto, Kazushige Terui, Dan Turetsky and more
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Artem Chernikov@archernikov11 Apr 2025
A new Ph.D thesis prize is being established in honor of Zoé Chatzidakis. This yearly award for an outstanding thesis in model theory will honor her scientific legacy and her commitment to the younger generation. helloasso.com/associations/f…
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A new Ph.D thesis prize is being established in honor of Zoé Chatzidakis. This yearly award for an outstanding thesis in model theory will honor her scientific legacy and her commitment to the younger generation. helloasso.com/associations/f…
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Artem Chernikov@archernikov7 Apr 2025
I'm excited to join the editorial board of a new diamond open access journal in mathematical logic: ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik zml.international/ The open letter of the editors of ZML can be found online on the webpage.
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I'm excited to join the editorial board of a new diamond open access journal in mathematical logic: ZML: Zeitschrift für Mathematische Logik und Grundlagen der Mathematik zml.international/ The open letter of the editors of ZML can be found online on the webpage.
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More on the collective action that led to the creation of this new journal: blog.tib.eu/2025/04/07/mlq-w…

Further resignation of an editorial board: Mathematical Logic Quarterly - TIB-Blog

There has been an increasing number of resignations by editors of scholarly journals in recent years. In many cases, the editors have criticised the publisher's excessive influence, especially when...

blog.tib.eu
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Another blog post on Retraction Watch about the Mathematical Logic Quarterly editorial board walk out, and the launch of a new diamond open access journal Zeitschrift für Mathematische Logik (ZML). retractionwatch.com/2025/04/…

Math journal editors resign to launch open-access title ‘free from pressure or influence’

The managing editors and entire editorial board of Mathematical Logic Quarterly, a Wiley title, have resigned, citing “unilateral decisions” by the publisher “that affected the editorial process.”&…

retractionwatch.com
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Retraction Watch blog post about the Mathematical Logic Quarterly editorial board walk out, and the launch of a new diamond open access journal Zeitschrift für Mathematische Logik (ZML).
Retraction Watch@RetractionWatch7 Apr 2025
Math journal editors resign to launch open-access title ‘free from pressure or influence’ retractionwatch.com/2025/04/…

Math journal editors resign to launch open-access title ‘free from pressure or influence’

The managing editors and entire editorial board of Mathematical Logic Quarterly, a Wiley title, have resigned, citing “unilateral decisions” by the publisher “that affected the editorial process.”&…

retractionwatch.com
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