Related papers: Introducing the hardline in proof theory
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
This paper presents the first in a series of results that allow us to develop a theory providing finer control over the complexity of normalisation, and in particular of cut elimination. By considering atoms as self-dual non-commutative…
In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.
We classify the stable formulas in the theory of Dense Linear Orders without endpoints, the stable formulas in the theory of Divisible Abelian Groups, and the stable formulas without parameters in the theory of Real Closed Fields. The third…
This paper deals with belief base revision that is a form of belief change consisting of the incorporation of new facts into an agent's beliefs represented by a finite set of propositional formulas. In the aim to guarantee more reliability…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
We describe the first results of a project of analyzing in which theories formal proofs can be ex- pressed. We use this analysis as the basis of interoperability between proof systems.
In the paper different kinds of proof of a given statement are discussed. Detailed descriptions of direct and indirect methods of proof are given. Logical models illustrate the essence of specific types of indirect proofs. Direct proofs of…
Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this paper, we will survey the use of structural proof theory as an alternative foundation. Researchers have been using…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
This article aims to explain essential elements of perturbation theory and their conceptual underpinnings. It is not meant as a summary of popular perturbation methods, though some illustrative examples are given to underline the main…
It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is possible to exhibit non-linearity and ill-foundedness by…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.
The foundations of forcing theory are reworked to streamline the presentation and to show how the most basic results are applicable in very general contexts.