Related papers: Un Crit{\`E}Re Simple

One of the key concepts in testing is that of adequate test sets. A test selection criterion decides which test sets are adequate. In this paper, a language schema for specifying a large class of test selection criteria is developed; the…

The reduced C*-algebra of a countable linear group G is shown to be simple if and only if G has no nontrivial normal amenable subgroups. Moreover, these conditions are shown to be equivalent to the uniqueness of tracial state on the…

Simple-minded systems of objects in a stable module category are defined by common properties with the set of simple modules, whose images under stable equivalences do form simple-minded systems. Over a representation-finite self-injective…

We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…

A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently…

We prove a version of Hrushovski's socle lemma for rigid groups in an arbitrary simple theory.

Let $I=[0,1)$ and $\mathcal{PC}(I)$ [resp. $\mathcal{PC}^+(I)$] be the quotient group of the group of all piecewise continuous [resp. piecewise continuous and orientation preserving] bijections of $I$ by its normal subgroup consisting in…

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a…

Let $A$ be an elementary abelian $r$-group with rank at least $3$ that acts faithfully on the finite $r'$-group $G$. Assume that $G$ is $A$-simple, so that $G = K_{1} \times\cdots\times K_{n}$ where $K_{1},\ldots,K_{n}$ is a collection of…

We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently, to another proof of the consistency of the axioms of the…

We prove Cuntz-Krieger and graded uniqueness theorems for Steinberg algebras. We also show that a Steinberg algebra is basically simple if and only if its associated groupoid is both effective and minimal. Finally we use results of…

Using the string field theory recently proposed by the authors and collaborators, we give a background independent formulation of rational noncritical string theories with $c\leq 1$. With a little modification of the string field…

We give a simple proof that the first-order theory of well orders is axiomatized by transfinite induction, and that it is decidable.

We describe a simple criterion for showing that a group has Serre's property FA. By exhibiting a certain pattern of finite subgroups, we show that this criterion is satisfied by Aut(F_n) and SL(n,Z) when n>=3.

This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence…

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…

Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…

Given a set X of finite strings, one interesting question to ask is whether there exists a member of X which is simple conditional to all other members of X. Conditional simplicity is measured by low conditional Kolmogorov complexity. We…

The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…