Finitely Supported Sets Containing Infinite Uniformly Supported Subsets

Infinities within Finitely Supported Structures

The theory of finitely supported algebraic structures is related to Pitts theory of nominal sets (by equipping finitely supported sets with finitely supported internal algebraic laws). It represents a reformulation of Zermelo Fraenkel set theory obtained by requiring every set theoretical construction to be finitely supported according to a certain action of a group of permutations of some basic elements named atoms. Its main purpose is to let us characterize infinite algebraic structures, defined involving atoms, only by analyzing their finite supports. The first goal of this paper is to defi…

A Finitely Supported Frame for the Turing Schmerl Calculus

In arXiv:1604.08705 we introduced the propositional modal logic $\textbf{TSC}$ (which stands for Turing Schmerl Calculus) which adequately describes the provable interrelations between different kinds of Turing progressions. In arXiv:1709.04715 we defined a model $\mathcal{J}$ which is proven to be a universal model for $\textbf{TSC}$ based on the intensively studied Ignatiev's universal model for the closed fragment of $\textbf{GLP}$ (Gödel Löb's polymodal provability logic). In the current paper we present a new universal frame $\mathcal{H}$, which is a slight modification of $\mathcal{J}$, …

A variety with solvable, but not uniformly solvable, word problem

In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if there is an algorithm which given a finite presentation produces an algorithm for solving the word problem of the algebra so presented. A variety is given with finitely many axioms having a decidable, but not uniformly decidable, word problem. Other related examples are given as well.

有限支撑结构的有限依赖与不变性层级

Finite Dependence and Invariance Hierarchies for Finitely Supported Structures

本文针对有限支撑结构提出有限依赖轮廓与不变性层级，揭示交律、并律等性质与最小支撑、轨道有限性及虚设消去等概念的联系。