Related papers: A characterization of ordinal analysis
The idea of meaning as use in language is explored in a mathematical and physical context. Two possible scenarios of further analysis are presented: Ordinal arithmetic and String theory.
Surprisal theory links human processing effort to the predictability of an upcoming linguistic unit, but empirical work often leaves the notion of a unit underspecified. In practice, experimental stimuli are segmented into linguistically…
We give another proof of ordinal analysis of $I\Sigma_{k}$-fragments of Peano Arithmetic which is free from cut-elimination of $\omega$-logic. Our main tool is a direct witnessing argument utilizing game notion, motivated from the realm of…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We prove a strengthened version of V. Yu. Shavrukov's result on the non-isomorphism of diagonalizable algebras of two $\Sigma_1$-sound theories, based on the improvements previously found by G. Adamsson. We then obtain several corollaries…
A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…
These are the lecture notes of an introductory course on ordinal analysis. Our selection of topics is guided by the aim to give a complete and direct proof of a mathematical independence result: Kruskal's theorem for binary trees is…
Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
We show that every separable simple tracially approximately divisible $C^*$-algebra has strict comparison, is either purely infinite, or has stable rank one. As a consequence, we show that every (non-unital) finite simple ${\cal Z}$-stable…
Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched,…
The focus of these lecture notes is on abstract models and basic ideas and results that relate to the operational semantics of programming languages largely conceived. The approach is to start with an abstract description of the computation…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
Necessary and sufficient conditions are given for the similarity between two perturbations of the (backward) shift by rank one operators, under certain assumptions on the perturbations. The proof of similarity is based on an explicit…
Two first-order logic theories are definitionally equivalent if and only if there is a bijection between their model classes that preserves isomorphisms and ultraproducts (Theorem 2). This is a variant of a prior theorem of van Benthem and…
In arXiv:2208.12944 it is shown that an ordinal $\sup_{N<\omega}\psi_{\Omega_{1}}(\varepsilon_{\Omega_{\mathbb{S}+N}+1})$ is an upper bound for the proof-theoretic ordinal of a set theory ${\sf KP}\ell^{r}+(M\prec_{\Sigma_{1}}V)$. In this…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…