Logical quantizations of first-order structures
type: Item
instance of: scholarly article
title: Logical quantizations of first-order structures
zbMATH Open document ID: 0867.03021
DOI: 10.1007/BF02082820
author: Hirokazu Nishimura
published in: International Journal of Theoretical Physics
publication date: 1997-08-04T00:00:00Z
review text: The paper is part of a long series of articles (published in Int. J. Theor. Phys., Vol. 31-35), concerning quantization of various mathematical structures. In this paper quantization of mathematical structures defined by so called limit theories is considered (including, e.g., posets and order-preserving mappings, or Banach spaces and contractive linear transformations). The author works with infinitary many-sorted first-order logics. Category theory is also used essentially. The paper is sufficiently characterized by an outline of the content, due to the author himself: ``Section 1 is devoted to a review of infinitary logic, sketches, accessible categories \dots . After limit sketches are Booleanized in Section 2, the relationship between two Booleanizations of limit sketches \dots is discussed in Section 3. The last section is devoted to quantizing limit sketches logically''.
Mathematics Subject Classification ID: 03G30
Mathematics Subject Classification ID: 03C75
Mathematics Subject Classification ID: 18F05
Mathematics Subject Classification ID: 81P10
zbMATH DE Number: 889797
zbMATH Keywords: Boolean locale
zbMATH Keywords: Booleanization
zbMATH Keywords: quantization
zbMATH Keywords: limit theories
zbMATH Keywords: infinitary many-sorted first-order logics
zbMATH Keywords: infinitary logic
zbMATH Keywords: accessible categories
zbMATH Keywords: limit sketches
reviewed by: Serguei V. Solov'ev
MaRDI profile type: Publication
cites work: Q4293501
cites work: Seminar of algebraic geometry du Bois-Marie 1963--1964. Topos theory and étale cohomology of schemes (SGA 4). Vol. 1: Topos theory. Exp. I--IV
cites work: Q3997112
cites work: Q5679011
cites work: Q4039735
cites work: Q4314472
cites work: Model theory
cites work: Large infinitary languages. Model theory
cites work: Lokal präsentierbare Kategorien. (Locally presentable categories)
cites work: Topoi. The categorial analysis of logic
cites work: Q4200260
cites work: Q4003410
cites work: Q3852172
cites work: Q3672155
cites work: FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES
cites work: Q4693151
cites work: Accessible Categories: The Foundations of Categorical Model Theory
cites work: First order categorical logic. Model-theoretical methods in the theory of topoi and related categories
cites work: Q4123496
cites work: Q3997818
cites work: An approach to the dimension theory of continuous geometry from the standpoint of Boolean valued analysis
cites work: Boolean valued Lie algebras
cites work: Boolean transfer from coherent quantum logics to quantum logics with continuous superselection rules
cites work: On the duality between Boolean-valued analysis and reduction theory under the assumption of separability
cites work: Empirical set theory
cites work: Representations of empirical set theories
cites work: Manuals in orthogonal categories
cites work: Empirical sets
cites work: The logical quantization of algebraic groups
cites work: Logical quantization of differential geometry
cites work: Boolean valued interpretation of Hilbert space theory
cites work: A classification of type I \(AW^*\)-algebras and Boolean valued analysis
cites work: A Transfer Principle from Von Neumann Algebras to AW∗ -Algebras
cites work: Q5612497
cites work: Q5666704
cites work: Commutative regular rings and Boolean-valued fields
cites work: Two Applications of Logic to Mathematics
description: scientific article; zbMATH DE number 889797