We describe an infinitary logic for metric structures which is analogous to Lω1,ω. We show that this logic is capable of expressing several concepts from analysis that cannot be expressed in finitary continuous logic. Using topological methods, we prove an omitting types theorem for countable fragments of our infinitary logic. We use omitting types to prove a two-cardinal theorem, which yields a strengthening of a result of Ben Yaacov and Iovino concerning separable quotients of Banach spaces.

By utilizing the topological concept of pseudocompactness, we simplify and improve a proof of Caicedo, Dueñez, and Iovino concerning Terence Tao's metastability. We also pinpoint the exact relationship between the Omitting Types Theorem and the Baire Category Theorem by developing a machine that turns topological spaces into abstract logics.

We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II1factor as Fraïssé limits of suitable classes of structures. Moreover by means of Fraïssé theory we provide new examples of AF algebras with strong homogeneity properties. As a consequence of our analysis we deduce Ramsey-theoretic results about the class of full-matrix algebras.

Work of Eagle, Farah, Goldbring, Kirchberg, and Vignati shows that the only separable C*‐algebras that admit quantifier elimination in continuous logic are,,, and the continuous functions on the Cantor set. We show that, among finite dimensional C*‐algebras, quantifier elimination does hold if the language is expanded to include two new predicate symbols: One for minimal projections, and one for pairs of unitarily conjugate elements. Both of these predicates are definable, but not quantifier‐free definable, in the usual language of C*‐algebras. We (...) also show that adding just the predicate for minimal projections is sufficient in the case of full matrix algebras, but that in general both new predicate symbols are required. (shrink)

We examine topological dynamical systems on the Cantor set from the point of view of the continuous model theory of commutative C*-algebras. After some general remarks, we focus our attention on the generic homeomorphism of the Cantor set, as constructed by Akin, Glasner, and Weiss. We show that this homeomorphism is the prime model of its theory. We also show that the notion of “generic” used by Akin, Glasner, and Weiss is distinct from the notion of “generic” encountered in Fraïssé (...) theory. (shrink)

In the Cratylus, Soc rates discusses with Cratylus and Hermogenes the question of whether names are merely arbitrary or in some sense ‘right,’ that is, motivated by the nature of the things they designate. In this article, I examine Heidegger’s controversial project of unearthing archē Greek terms in the specific light of the Cratylus and the tradition of “Cratylisms” which it has fostered. Having demonstrated the underlying Cratylist tendencies behind Heidegger’s conviction in the inherent ‘appropriateness’ of many Greek keywords, I (...) point out some of the problems posed by this closet Cratylism for Heidegger’s conception of primordial language as well as his critique of the correspondence theory of truth. (shrink)

In the Cratylus, Soc rates discusses with Cratylus and Hermogenes the question of whether names are merely arbitrary or in some sense ‘right,’ that is, motivated by the nature of the things they designate. In this article, I examine Heidegger’s controversial project of unearthing archē Greek terms in the specific light of the Cratylus and the tradition of “Cratylisms” which it has fostered. Having demonstrated the underlying Cratylist tendencies behind Heidegger’s conviction in the inherent ‘appropriateness’ of many Greek keywords, I (...) point out some of the problems posed by this closet Cratylism for Heidegger’s conception of primordial language as well as his critique of the correspondence theory of truth. (shrink)