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Predicativity and Regions-Based Continua

  • Geoffrey Hellman
  • Stewart Shapiro
Chapter
Part of the Outstanding Contributions to Logic book series (OCTR, volume 13)

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.

Keywords

Continuity Predicativity Point-free Constructive Infinity 

2010 Mathematics Subject Classification

03A05 03B20 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of PhilosophyThe Ohio State UniversityColumbusUSA

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