Related papers: Friedman-reflexivity: interpreters as consistoids

The robustness property of exponential dichotomies refers to the stability of this notion under small linear perturbations. In recent work~\cite{PPX}, the authors have identified a new class of perturbations under which the notion of a…

In the following paper we propose a model-theoretical way of comparing the "strength" of various truth theories which are conservative over PA. Let $\mathfrak{Th}$ denote the class of models of PA which admit an expansion to a model of…

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…

We offer a mathematical proof of consistency for Peano Arithmetic PA formalizable in PA. This result is compatible with Goedel's Second Incompleteness Theorem since our consistency proof does not rely on the representation of consistency as…

We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…

We prove upper and lower bounds on the effective content and logical strength for a variety of natural restrictions of Hindman's Finite Sums Theorem. For example, we show that Hindman's Theorem for sums of length at most 2 and 4 colors…

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…

We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic…

We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…

We present a new strictification method for type-theoretic structures that are only weakly stable under substitution. Given weakly stable structures over some model of type theory, we construct equivalent strictly stable structures by…

Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of…

The $U^2$ norm gives a useful measure of quasirandomness for real- or complex-valued functions defined on finite (or, more generally, locally compact) groups. A simple Fourier-analytic argument yields an inverse theorem, which shows that a…

In Team Semantics, a dependency notion is strongly first order if every sentence of the logic obtained by adding the corresponding atoms to First Order Logic is equivalent to some first order sentence. In this work it is shown that all…

Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…

The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…

We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. We prove that an implication of Fuchino-Usuba relating stationary reflection to a version of Strong Chang's Conjecture cannot…

This work proposes a new a framework for determining robust periodic invariant sets and their associated control laws for constrained uncertain linear systems. Necessary and sufficient conditions for stabilizability by periodic controllers…

This paper investigates asymptotic fixed point results for nonlinear contractions, with emphasis on Kirk-type theorems and their generalizations. A central difficulty in the literature has been the requirement that the mapping possesses a…