Model theory for metric structures

Reduced Products of Metric Structures: A Metric Feferman–vaught Theorem

“…Logic for metric structures. A main reference for logic for metric structures is [2], see also [19]. A metric structure, in the sense of [2], is a many-sorted structure in which each sort is a complete bounded metric space.…”

Locally compact groups which are separably categorical structures

“…For convenience of the reader we recall some basic definitions from [3] and [4]. We keep the signature L together with functions γ 1 …”

“…Let acl(A) be the set of all elements algebraic over A. In continuous logic the concept of algebraicity is parallel to that in traditional model theory (see Section 10 of [3]). …”

“…By Theorem 12.10 of [3] a complete theory T is separably categorical if and only if for each n > 0, every n-type p is principal. The latter means that for every model M | T , the predicate dist (x, p(M)) is definable over ∅.…”

Isomorphisms of quotients of FDD-algebras

“…Since the corona of n M n (C) is fully countably saturated structure in the sense of the model theory for metric structures (see [3] and [12]) and its character density (the smallest cardinality of a dense subset) is the continuum, under CH it is possible to use a diagonalization argument to show that there are 2 ℵ 1 automorphisms of each of these corona algebras. Therefore there are many non-trivial automorphisms (see [11], §2.4).…”