10 citations · 40 across the 18 of their papers we have counts for
18 papers
Keisler Measures and Generically Stable Random Types
Karim Khanaki
We introduce the notions of and for Keisler measures, motivated by the study of generically stable random types and their associated Morley sequences. We obtain charac…
Simple Models of Randomization and Preservation Theorems
Karim Khanaki, Massoud Pourmahdian
The main purpose of this paper is to present a new and more uniform model-theoretic/combinatorial proof of the theorem ([5]): The randomization of a complete first-order th…
Grothendieck's Double Limit Theorem and Model Theory
Karim Khanaki
This is an expository paper in Persian on Grothendieck's double limit theorem and its connection with the (neo-)stability project. We review recent results/observations and discuss…
On classification of continuous first order theories
Karim Khanaki
We give several new characterizations of (the independence property) and (the strict order property) for continuous first order logic and study their relations to the fu…
Generic Stability and Modes of Convergence
Karim Khanaki
We study generically stable types/measures in both classical and continuous logics, and their connection with randomization and modes of convergence of types/measures.
Remarks on convergence of Morley sequences
Karim Khanaki
We refine results of Gannon [G21, Theorem 4.7] and Simon [S15a, Lemma 2.8] on equivalences of convergent Morley sequences. We then introduce the notion of eventual , as a prop…
Dependent measures in independent theories
Karim Khanaki
We introduce the notion of dependence, as a property of a Keisler measure, and generalize several results of [HPS13] on generically stable measures (in theories) to arbitrary…
Glivenko-Cantelli classes and NIP formulas
Karim Khanaki
We give several new equivalences of for formulas and new proofs of known results using [T87] and [HOR91]. We emphasize that Keisler measures are more complicated than types (…
Dividing lines in unstable theories and subclasses of Baire 1 functions
Karim Khanaki
We give a new characterization of (the strict order property) in terms of the behaviour of formulas in any model of the theory as opposed to having to look at the behaviour o…
Continuous logic and the strict order property
Karim Khanaki
We generalize a theory of Shelah for continuous logic, namely a continuous theory has OP if and only if it has IP or SOP.
Remarks on Banach spaces determined by their finite dimensional subspaces
Karim Khanaki
A separable Banach space is said to be finitely determined if for each separable space such that is finitely representable (f.r.) in and is f.r. in then …
Remarks on NIP in a model
Karim Khanaki, Anand Pillay
We define the notion has in , where is a subset of a model, and give some equivalences by translating results from [1]. Using additional material from [11] we…
NIP formulas and Baire 1 definability
Karim Khanaki
In this short note, using results of Bourgain, Fremlin, and Talagrand \cite{BFT}, we show that for a countable structure , a saturated elementary extension of and a fo…
-categorical Banach spaces contain or
Karim Khanaki
This paper has three parts. First, we establish some of the basic model theoretic facts about , the Tsirelson space of Figiel and Johnson \cite{FJ}. Second, using…
Correspondences between model theory and Banach space theory
Karim Khanaki
In \cite{K3} we pointed out the correspondence between a result of Shelah in model theory, i.e. a theory is unstable if and only if it has IP or SOP, and the well known compactness…
Eberlein-Smulian compactness and Kolmogorov extension theorems; a model theoretic approach
Seyed-Mohammad Bagheri, Karim Khanaki
This paper has two parts. First, we complete the proof of the Kolmogorov extension theorem for unbounded random variables using compactness theorem of integral logic which was prov…
Stability, NIP, and NSOP; Model Theoretic Properties of Formulas via Topological Properties of Function Spaces
Karim Khanaki
We study and characterize stability, NIP and NSOP in terms of topological and measure theoretical properties of classes of functions. We study a measure theoretic property, `Talagr…
Amenability, extreme amenability, model-theoretic stability, and dependence property in integral logic
Karim Khanaki
This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove de…