Stability, the NIP, and the NSOP: model theoretic properties of formulas via topological properties of function spaces

Khanaki, Karim

doi:10.1002/malq.201500059

Cited by 11 publications

(33 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, if we fix some measure on the parameter space, any sequentially approximated measure is almost finitely approximated. This result is in a similar vein to Khanaki's almost definable coheirs in the local setting [13]. A direct application of Egorov's theorem gives our result.…”

Section: Keisler Measuressupporting

confidence: 81%

Sequential approximations for types and Keisler measures

Gannon

2022

Fund. Math.

View full text Add to dashboard Cite

This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a sequence of realized types and measures which can be approximated by a sequence of "averaging measures" on tuples of realized types. We show that both generically stable types (in arbitrary theories) and Keisler measures which are finitely satisfiable over a countable model (in NIP theories) are sequentially approximated. We also introduce the notion of a smooth sequence in a measure over a model and give an equivalent characterization of generically stable measures (in NIP theories) via this definition. In the last section, we take the opportunity to generalize the main result of our 2019 paper in J. Symbolic Logic.

show abstract

Section: Keisler Measuressupporting

confidence: 81%

Sequential approximations for types and Keisler measures

Gannon

2022

Fund. Math.

View full text Add to dashboard Cite

show abstract

“…Hence it is Grothendieck and countably tight and thus our results apply. 5 The NIP and the Bourgain-Fremlin-Talagrand Dichotomy A series of papers by P. Simon [33], K. Khanaki [22,23] and Khanaki and A. Pillay [24] has explored connections between the Non Independence Property (NIP) and the famous dichotomy of [6]:…”

Section: Applications and Examples Concerning The Undefinability Of Pathological Banach Spacesmentioning

confidence: 99%

Model theory for Cp-theorists

Hamel¹,

Tall²

2020

Topology and its Applications

View full text Add to dashboard Cite

We present applications of C p -theory, the branch of general topology concerned with spaces of real-valued continuous functions, to model theory, mostly in the context of continuous logics. We include C p -theoretic results and proofs in a self-contained way for model theorists who are not familiar with the techniques of this field. We further generalize some results of Casazza and Iovino, and of the authors, involving the definability of Banach spaces including isomorphic copies of c 0 or ℓ p , after a problem posed by Odell and Gowers.

show abstract

“…The current paper is partly expository, and has thematic overlap with . The notion of “the NIP of

φ (x, y)

in a model” is mentioned in . But deal with “the NIP of

φ (x, y)

in a theory” (in the continuous framework in the latter paper).…”

Section: Introductionmentioning

confidence: 99%

“…It has been known for a long time that the notion of the NIP arose independently in model theory and learning theory . More recently it was noticed by several people (e.g., ) that the notion also appeared independently in the context of function spaces . The latter paper was at a fairly high level of generality due to trying to find a common context for functions on compact (Hausdorff) spaces and functions on Polish spaces.…”

Section: Introductionmentioning

confidence: 99%