Related papers: An Introduction To Continuous Model Theory
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…
Ultraproducts are a well-known tool in the classical model theory of first-order logic. We explore their uses in the context of finite model theory.
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…
We give a classification theorem for a class of C*-algebras which are direct limits of extensions of circle algebras by purely infinite C*-algebras. The invariant consists of the following: (1) the set of Murray-von Neumann equivalence…
We survey the model theory of operator systems and C$^*$-algebras.
This thesis is dedicated to developing a dilation theory for semigroups of completely positive maps. The first part treats two-parameter semigroups, and contains also contributions to dilation theory of product system representations. The…
A universal C*-algebra of the electromagnetic field is constructed. It is represented in any quantum field theory which incorporates electromagnetism and expresses basic features of this field such as Maxwell's equations, Poincar\'e…
In this course we introduce the main notions relative to the classical theory of modular forms. A complete treatise in a similar style can be found in the author's book joint with F. Str{\"o}mberg [1].
We survey various attempts to transport the ultraproduct construction from the realm of model theory to that of general topology.
We generalize some basic C*-algebra and von Neumann algebra theory on hereditary C*-subalgebras and projections. In particular, we extend Murray-von Neumann equivalence from projections to *-annihilators and show that several of its…
This paper collates, presents, and expands upon technology and results obtained as part of the author's PhD thesis. We generalize work done in the $\sigma$-finite setting by the author, Goldbring, Hart, and Sinclair by producing a language…
This is a study of universal problems for semimodules, in particular coequalizers, coproducts, and tensor products. Furthermore the structure theory of semiideals of the semiring of natural numbers is extended.
The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\Omega$ of objects belonging…
Notions of topological free entropy and of free capacity are introduced in the $C^*$-algebra context. Basic properties, basic problems and connections to potential theory and random matrix theory are discussed.
We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Determinantal formulas, relation to conformal field models and the theory of Generalized Kontsevich model are discussed in some…
Cuntz and Li have defined a C*-algebra associated to any integral domain, using generators and relations, and proved that it is simple and purely infinite and that it is stably isomorphic to a crossed product of a commutative C*-algebra. We…
This paper presents a novel possible worlds semantics, designed to elucidate the underpinnings of ultrafinitism. By constructing a careful modification of the well-known Kripke models for inuitionistic logic, we seek to extend our…
We combine continuous and integral logics and found a logical framework for metric measure spaces equipped with a family of continuous relations and operations. We prove the ultraproduct theorem and deduce compactness and other usual…
Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…