Related papers: Generic derivations on o-minimal structures
We show that the theories of some (ordered) central simple algebras with involution over real closed fields are model-complete or admit quantifier elimination, and characterize positive cones in terms of morphisms into models of some of…
The linear Reissner-Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC) using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach.…
Let $(M,\scott X) \models \ACA$ be such that $P_\scott X$, the collection of all unbounded sets in $\scott X$, admits a definable complete ultrafilter and let $T$ be a theory extending first order arithmetic coded in $\scott X$ such that…
In this thesis the recently developed duality covariant approach to string and M-theory is investigated. In this formalism the U-duality symmetry of M-theory or T-duality symmetry of Type II string theory becomes manifest upon extending…
Motivated by the two-dimensional massive gravity description of $T\overline{T}$ deformations, we propose a direct generalization in $d$ dimensions. Our methodology indicates that all terms up to order $d$ are present in the deformation. In…
In this paper, we focus on the $(\si,\t)$-derivation theory of Lie conformal superalgebras. Firstly, we study the fundamental properties of conformal $(\si,\t)$-derivations. Secondly, we mainly research the interiors of conformal…
If $\mathcal{L}$ is an abstract logic (a.k.a. model theoretic logic), we can define the inner model $C(\mathcal{L})$ by replacing first order logic with $\mathcal{L}$ in G\"odel's definition of the inner model $L$ of constructible sets. Set…
This paper is devoted to derivations on the algebra $S_0(M, \tau)$ of all $\tau$-compact operators affiliated with a von Neumann algebra $M$ and a faithful normal semi-finite trace $\tau.$ The main result asserts that every…
For certain theories of existentially closed topological differential fields, we show that there is a strong relationship between $\mathcal L\cup\{D\}$-definable sets and their $\mathcal L$-reducts, where $\mathcal L$ is a relational…
We go on in the program of investigating the removal of divergences of a generical quantum gauge field theory, in the context of the Batalin-Vilkovisky formalism. We extend to open gauge-algebrae a recently formulated algorithm, based on…
We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the…
Open-closed Deligne--Mumford field theories are chain-level field theories based on moduli spaces of stable curves with boundary. We associate to a relatively spin embedded Lagrangian $L \subset (X,\omega)$ such an open-closed DMFT. It…
We let R be an o-minimal expansion of a field, V a convex subring, and $(R_0, V_{0})$ an elementary substructure of (R,V). We let L be the language consisting of a language for R, in which R has elimination of quantifiers, and a predicate…
We discuss ways of adjoining perfect sets of mutually generic random reals. In particular, we show that if V \sub W are models of ZFC and W contains a dominating real over V, then W[r], where r is random over W, contains a perfect tree of…
We introduce the subject of modal model theory, where one studies a mathematical structure within a class of similar structures under an extension concept that gives rise to mathematically natural notions of possibility and necessity. A…
The irrelevant composite operator $T\bar{T}$, constructed from components of the stress-energy tensor, exhibits unique properties in two-dimensional quantum field theories and represents a distinctive form of integrable deformation.…
Deep generative models aim to learn the underlying distribution of data and generate new ones. Despite the diversity of generative models and their high-quality generation performance in practice, most of them lack rigorous theoretical…
Recent progress in generalised geometry and extended field theories suggests a deep connection between consistent truncations and dualities, which is not immediately obvious. A prime example is generalised Scherk-Schwarz reductions in…
Let $G$ be a reductive algebraic group---possibly non-connected---over a field $k$ and let $H$ be a subgroup of $G$. If $G= GL_n$ then there is a degeneration process for obtaining from $H$ a completely reducible subgroup $H'$ of $G$; one…
We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two…