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Amenability and Ramsey theory in the metric setting

Adriane Kaïchouh (2015)

Fundamenta Mathematicae

Moore [Fund. Math. 220 (2013)] characterizes the amenability of the automorphism groups of countable ultrahomogeneous structures by a Ramsey-type property. We extend this result to the automorphism groups of metric Fraïssé structures, which encompass all Polish groups. As an application, we prove that amenability is a G δ condition.

Categoricity without equality

H. Jerome Keisler, Arnold W. Miller (2001)

Fundamenta Mathematicae

We study categoricity in power for reduced models of first order logic without equality.

Classification Trees as a Technique for Creating Anomaly-Based Intrusion Detection Systems

Jecheva, Veselina, Nikolova, Evgeniya (2009)

Serdica Journal of Computing

Intrusion detection is a critical component of security information systems. The intrusion detection process attempts to detect malicious attacks by examining various data collected during processes on the protected system. This paper examines the anomaly-based intrusion detection based on sequences of system calls. The point is to construct a model that describes normal or acceptable system activity using the classification trees approach. The created database is utilized as a basis for distinguishing...

On d-finite tuples in random variable structures

Shichang Song (2013)

Fundamenta Mathematicae

We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.

On d-finiteness in continuous structures

Itaï Ben Yaacov, Alexander Usvyatsov (2007)

Fundamenta Mathematicae

We observe that certain classical results of first order model theory fail in the context of continuous first order logic. We argue that this happens since finite tuples in a continuous structure may behave as infinite tuples in classical model theory. The notion of a d-finite tuple attempts to capture some aspects of the classical finite tuple behaviour. We show that many classical results involving finite tuples are valid in continuous logic upon replacing "finite" with "d-finite". Other results,...

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