Related papers: Peano Arithmetic may not be interpretable in the m…
To answer a question by Rettich and Serafin, we define a model of set theory in which there exists a locally countable $\varPi^1_2$ graph on a subset of the real line, which is not generated by a countable family of projective (or even…
A formalisation of G\"odel's incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows {\'S}wierczkowski…
Throughout the course of mathematical history, generalizations of previously understood concepts and structures have led to the fruitful development of the hierarchy of number systems, non-euclidean geometry, and many other epochal phases…
We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality…
Type two cuts, bad cuts and very bad cuts are introduced by Keisler and Leth for studying the relationship between Loeb measure and U-topology of a hyperfinite time line in an $\omega_1$-saturated nonstandard universe. The questions…
We show spherical completeness of the ring of Colombeau generalized real (or complex) numbers endowed with the sharp norm. As an application, we establish a Hahn Banach extension theorem for ultra pseudo normed modules (over the ring of…
We show that the first order theory of the homeomorphism group of a compact manifold interprets the full second order theory of countable groups of homeomorphisms of the manifold. The interpretation is uniform across manifolds of bounded…
We compare classes of finite relational structures via monadic second-order transductions. More precisely, we study the preorder where we set C \subseteq K if, and only if, there exists a transduction {\tau} such that C\subseteq{\tau}(K).…
We give conditions for local diagonalization of analytic operator families acting between real or complex Banach spaces. The transformations are constructed from an operator Toeplitz matrix obtained from Jordan chains of increasing length.…
We investigate the extent of second order characterizable structures by extending Shelah's Main Gap dichotomy to second order logic. For this end we consider a countable complete first order theory T. We show that all sufficiently large…
Courcelle's Theorem states that on graphs $G$ of tree-width at most $k$ with a given tree-decomposition of size $t(G)$, graph properties $\mathcal{P}$ definable in Monadic Second Order Logic can be checked in linear time in the size of…
An elementary rheory of concatenation is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, the quantifier-free part of Kirby's finitary set theory, and Adjunctive Set Theory,…
In a previous work we introduced an elementary method to analyze the periodicity of a generating function defined by a single equation y=G(x,y). This was based on deriving a single set-equation Y = Gammma(Y) defining the spectrum of the…
Let $\mathbb F$ be an algebraically closed field of characteristic $p\ge 0$, which is complete with respect to a non-Archimedean absolute value. Let $V$ be a projective subvariety of $\mathbb P^M(\mathbb F)$. In this paper, we will prove…
For a (minimal) Arithmetical theory with higher Order Objects, i.e. a (minimal) Cartesian closed arithmetical theory -- coming as such with the corresponding closed evaluation -- we interprete here map codes, out of [A,B] say,into these…
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always…
Using a direct algebraic approach we derive convolution identities for second order sequences, hereby distinguishing between sequences obeying the same or different recurrence relations. We also state a general convolution for Horadam…
By combining classical results of B\"uchi, some elementary Tauberian theorems and some basic tools from logic and combinatorics we show that every ordinal $\alpha$ with $\varepsilon_0\geq \alpha\geq \omega^\omega$ satisfies a natural…
Convexity is an important notion in non linear optimization theory as well as in infinite dimensional functional analysis. As will be seen below, very simple and powerful tools will be derived from elementary duality arguments (which are…
We study the Dunkl-Opdam subalgebra of the rational Cherednik algebra for wreath products at $t=0$, and use this to describe the block decomposition of restricted rational Cherednik algebras for $G(m,d,n)$.