Some connections between Heyting valued set theory and algebraic geometry. Prolegomena to intuitionistic algebraic geometry
type: Item
instance of: scholarly article
title: Some connections between Heyting valued set theory and algebraic geometry. Prolegomena to intuitionistic algebraic geometry
zbMATH Open document ID: 0662.03048
author: Hirokazu Nishimura
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1987-01-01T00:00:00Z
review text: \textit{C. Rosseau} [Lect. Notes Math. 753, 623-659 (1979; Zbl 0433.32003)] has shown that classical or standard function theory of n variables is no other than intuitionistic function theory of one variable over \(C^{n- 1}\). Similar works have been done by the author [Publ. Res. Inst. Math. Sci. 22, 801-811 (1986; Zbl 0614.03058)] in the realm of Sato hyperfunctions and by \textit{G. Takeuti} and \textit{S. Titani} [Ann. Pure Appl. Logic 31, 307-339 (1986; Zbl 0615.03048)] in the realm of complex manifolds. The main purpose of this paper is to pursue similar results in the arena of algebraic geometry. Since we would like to do so in an intuitionistically valid manner, we reconstruct some rudiments of algebraic geometry, using the complete Heyting algebra of radical ideals in place of the space of prime ideals with Zariski topology as the starting point of our scheme theory.
reviewed by: Hirokazu Nishimura
Mathematics Subject Classification ID: 03E70
Mathematics Subject Classification ID: 03F55
Mathematics Subject Classification ID: 14A99
zbMATH DE Number: 4081549
zbMATH Keywords: Heyting valued set theory
zbMATH Keywords: algebraic geometry
zbMATH Keywords: complete Heyting algebra of radical ideals
zbMATH Keywords: scheme theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195176443
OpenAlex ID: W2057147820
cites work: Q3050433
cites work: Q5658173
cites work: Q4143433
cites work: Rings, fields, and spectra
cites work: Q4138872
cites work: Heyting valued set theory and Sato hyperfunctions
cites work: Q3871177
cites work: Q5732721
DOI: 10.2977/PRIMS/1195176443
Recommended article: Some corrections on my paper ``Some connections between Heyting valued set theory and algebraic geometry: Prolegomena to intuitionistic algebraic geometry''
Recommended article: Q4694208
Recommended article: Intuitionistic theory of algebraic systems and the Heyting-valued analysis
Recommended article: Heyting valued set theory and Sato hyperfunctions
Recommended article: On the Heyting algebra objects in a topos
Recommended article: Q4237282
Recommended article: Algebraic Geometry over Heyting Algebras
Recommended article: Heyting valued set theory and fibre bundles
Recommended article: On set-theoretic intersections and connectedness of algebraic varieties in \(\mathbb P^n\)
Recommended article: Q4695117
description: scientific article; zbMATH DE number 4081549