Structures subject to space complexity

Complexity Theory has been applied to Model Theory and Algebra by Nerode, Cenzer, Remmel, and others. In their studies, the primary focus has been on polynomial-time complexity and other notions of bounded time. We now examine the notions of bounded space complexity in Algebra and Model theory. Of particular interest are the classes of logarithmic-space, linear-space, and polynomial-space computable sets and functions.