Abstract Let $G$ be a connected linear algebraic group over number field $K$, let $\Gamma $ finitely generated Zariski dense subgroup of $G(K)$, and $Z\subseteq G(K)$ thin set, in the sense Serre. We prove that, if $G/\textrm {R}_{u}(G)$ is either trivial or semisimple $Z$ satisfies certain necessary conditions, then long random walk on Cayley graph hits elements with negligible probability. de...

Kriegel's self-representationalist (SR) theory of phenomenal consciousness pursues two projects. The first is to offer a positive account of how conscious experience arises from physical brain processes. The second is to explain why consciousness misleadingly appears to be irreducible to the physical i.e. to 'demystify' consciousness. This paper seeks to determine whether SR succeeds on the sec...

This paper studies completion in the case of equations with constraints consisting of rstorder formulae over equations, disequations, and an irreducibility predicate. We present several inference systems which show in a very precise way how to take advantage of redundancy notions in this framework. A notable feature of these systems is the variety of tradeo s they present for removing redundant...