An Algebraization of Linear Continuum Structures

This paper continuous the approach of developing an ordertheoretic structure theory of one-dimensional continuum structures as elaborated in [Wi07] (see also [Wi83],[Wi03]). The aim is to extend the order-theoretic structure theory by a meaningful algebraization; for this, we concentrate on the real linear continuum structure with its derived concept lattice which gives rise to the so-called “real half-numbers”. The algebraization approaches an ordered algebraic structure on the set of all real half-numbers to make the continuum structure of the reals more transparent and tractable.