Title

On the First-order Expressibility of Lattice Properties to Unicoherence in Continua

Document Type

Article

Publication Date

2011

Source Publication

Archive for Mathematical Logic

Abstract

Many properties of compacta have “textbook” definitions which are phrased in lattice-theoretic terms that, ostensibly, apply only to the full closed-set lattice of a space. We provide a simple criterion for identifying such definitions that may be paraphrased in terms that apply to all lattice bases of the space, thereby making model-theoretic tools available to study the defined properties. In this note we are primarily interested in properties of continua related to unicoherence; i.e., properties that speak to the existence of “holes” in a continuum and in certain of its subcontinua.

Comments

Archive for Mathematical Logic, Volume 50, Numbers 3-4, pp 503-512. DOI: 10.1007/s00153-011-0229-8