skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • Home
  • Search Results
  • Page 1 of 2

Search for: All records

Creators/Authors contains: "Chernikov, Artem"

Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher. Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?

Some links on this page may take you to non-federal websites. Their policies may differ from this site.

  1. ; (, Proceedings of the 14th Panhellenic Logic Symposium)
    Kavvos, Alex; Gregoriades, Vassilis (Ed.)
    For n∈ℕ and ε>0, given a sufficiently long sequence of events in a probability space all of measure at least ε, some n of them will have a common intersection. A more subtle pattern: for any 0<1, we cannot find events Ai and Bi so that μ(Ai∩Bj)≤p and μ(Aj∩Bi)≥q for all 1 
    more » « less
    Accepted Manuscript Full Text Available
  2. ; (, 14th Panhellenic Logic Symposium)
    For n ∈ N and ε > 0, given a sufficiently long sequence of events in a probability space all of measure at least ε, some n of them will have a common intersection. A more subtle pattern: for any 0 < p < q < 1, we cannot find events Ai and Bi so that μ (Ai ∩ Bj ) ≤ p and μ (Aj ∩ Bi ) ≥ q for all 1 < i < j < n, assuming n is sufficiently large. This is closely connected to model-theoretic stability of probability algebras. We survey some results from our recent work in [7] on more complicated patterns that arise when our events are indexed by multiple indices. In particular, how such results are connected to higher arity generalizations of de Finetti’s theorem in probability, structural Ramsey theory, hypergraph regularity in combinatorics, and model theory. 
    more » « less
    Accepted Manuscript Full Text Available
  3. ; ; (, Duke Mathematical Journal)
    Full Text Available 
  4. ; (, The Journal of Symbolic Logic)
    Abstract We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate. 
    more » « less
    Full Text Available 
  5. ; ; (, The Journal of Symbolic Logic)
    Abstract We develop the theory of Kim-independence in the context of NSOP $$_{1}$$ theories satisfying the existence axiom. We show that, in such theories, Kim-independence is transitive and that -Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP $$_{1}$$ theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP $$_{1}$$ theories. 
    more » « less
    Full Text Available 
  6. ; ; ; ; ; ; (, Journal of Mathematical Logic)
    We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. 
    more » « less
    Full Text Available 
  7. ; (, Model Theory)
    Full Text Available 
  8. ; (, Pacific Journal of Mathematics)
    Full Text Available 
  9. ; (, Israel Journal of Mathematics)
    Full Text Available 
  10. ; ; ; (, Transactions of the American Mathematical Society)
    Full Text Available