The classical continuum without points

Review of Symbolic Logic 6 (3):488-512 (2013)
Abstract
We develop a point-free construction of the classical one-dimensional continuum, with an interval structure based on mereology and either a weak set theory or a logic of plural quantification. In some respects, this realizes ideas going back to Aristotle, although, unlike Aristotle, we make free use of contemporary . Also, in contrast to intuitionistic analysis, smooth infinitesimal analysis, and Eret Bishopgunky lineindecomposabilityCantor structure of ℝ as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own
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References found in this work BETA
Hellman Geoffrey (1996). Structuralism Without Structures. Philosophia Mathematica 4 (2):100-123.
Peter Roeper (2006). The Aristotelian Continuum. A Formal Characterization. Notre Dame Journal of Formal Logic 47 (2):211-232.
Peter Roeper (1997). Region-Based Topology. Journal of Philosophical Logic 26 (3):251-309.
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