Formal Zariski topology: positivity and points

Annals of Pure and Applied Logic 137 (1-3):317-359 (2006)
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Abstract

The topic of this article is the formal topology abstracted from the Zariski spectrum of a commutative ring. After recollecting the fundamental concepts of a basic open and a covering relation, we study some candidates for positivity. In particular, we present a coinductively generated positivity relation. We further show that, constructively, the formal Zariski topology cannot have enough points

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10.1016/j.apal.2005.05.026

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Peter Schuster
University of Leeds

Citations of this work

Constructive mathematics.Douglas Bridges - 2008 - Stanford Encyclopedia of Philosophy.
A constructive investigation of satisfiability.Francesco Ciraulo - 2012 - Annals of Pure and Applied Logic 163 (2):111-121.
A constructive semantics for non-deducibility.Francesco Ciraulo - 2008 - Mathematical Logic Quarterly 54 (1):35-48.

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References found in this work

Varieties of constructive mathematics.Douglas Bridges & Fred Richman - 1987 - New York: Cambridge University Press. Edited by Fred Richman.
Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):461-461.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Mathematical Logic Quarterly 24 (25‐30):461-461.

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