Predicativity and Regions-Based Continua

Abstract

After recapitulating in summary form our basic regions-based theory of the classical one-dimensional continuum (which we call a semi-Aristotelian theory), and after presenting relevant background on predicativity in foundations of mathematics, we consider what adjustments would be needed for a predicative version of our regions-based theory, and then we develop them. As we’ll see, such a predicative version sits between our semi-Aristotelian system and an Aristotelian one, as well as falling generally between fully constructive and fully classical theories. Finally, we compare the resulting predicative theory and our original semi-Aristotelian one with respect to their power and unity.