Generic undecidability of universal theories

Undecidability of the Theories of Classes of Structures

Many classes of structures have natural functions and relations on them: concatentation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for...

Hereditary Undecidability of Some Theories of Finite Structures

Using a result of Gurevich and Lewis on the word problem for finite semigroups, we give short proofs that the following theories are hereditarily undecidable: (1) finite graphs of vertex-degree at most 3; (2) finite nonvoid sets with two distinguished permutations; (3) finitedimensional vector spaces over a finite field with two distinguished endomorphisms.

On the strongly generic undecidability of the Halting Problem

Generic Universal Switch Blocks

A switch block M with W terminals on each side is said to be universal if every set of nets satisfying the dimension constraint (i.e., the number of nets on each side of M is at most W ) is simultaneously routable through M [2]. In this paper, we present an algorithm to construct N -sided universal switch blocks with W terminals on each side. Each of our universal switch blocks has N2 W switche...

A New Method for Undecidability Proofs of First Order Theories

We claim that the reduction of Post's Correspondence Problem to the decision problem of a theory provides a useful tool for proving undecidability of rst order theories given by some interpretation. The goal of this paper is to deene a framework for such reduction proofs. The method proposed is illustrated by proving the undecidability of the theory of a term algebra modulo the axioms of associ...