## The Stone Gamut: A Coordinatization of Mathematics (1995)

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Venue: | In Logic in Computer Science |

Citations: | 30 - 13 self |

### BibTeX

@INPROCEEDINGS{Pratt95thestone,

author = {Vaughan R. Pratt},

title = {The Stone Gamut: A Coordinatization of Mathematics},

booktitle = {In Logic in Computer Science},

year = {1995},

pages = {444--454}

}

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### Abstract

We give a uniform representation of the objects of mathematical practice as Chu spaces, forming a concrete self-dual bicomplete closed category and hence a constructive model of linear logic. This representation distributes mathematics over a two-dimensional space we call the Stone gamut. The Stone gamut is coordinatized horizontally by coherence, ranging from \Gamma1 for sets to 1 for complete atomic Boolean algebras (CABA's), and vertically by complexity of language. Complexity 0 contains only sets, CABA's, and the inconsistent empty set. Complexity 1 admits noninteracting set-CABA pairs. The entire Stone duality menagerie of partial distributive lattices enters at complexity 2. Groups, rings, fields, graphs, and categories have all entered by level 16, and every category of relational structures and their homomorphisms eventually appears. The key is the identification of continuous functions and homomorphisms, which puts StonePontrjagin duality on a uniform basis by merging algebra...