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  1. A500 情報学部/情報学研究科・情報文化学部・情報科学研究科
  2. A500a 雑誌掲載論文
  3. 学術雑誌

ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY

http://hdl.handle.net/2237/00027943
http://hdl.handle.net/2237/00027943
b2782b37-ee7c-4fea-9154-e572ad5e681c
名前 / ファイル ライセンス アクション
MO170514_ppt.pdf MO170514_ppt (171.7 kB)
Item type 学術雑誌論文 / Journal Article(1)
公開日 2018-05-08
タイトル
タイトル ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY
言語 en
著者 OZAWA, MASANAO

× OZAWA, MASANAO

WEKO 76304

en OZAWA, MASANAO

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アクセス権
アクセス権 open access
アクセス権URI http://purl.org/coar/access_right/c_abf2
権利
言語 en
権利情報 This article has been published in a revised form in [The Review of Symbolic Logic] [https://doi.org/10.1017/S1755020317000120]. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2017 Cambridge University Press.
抄録
内容記述 In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo–Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti’s model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which asserts that every theorem in ZFC set theory holds in the models, to a general form holding in every orthomodular-valued model. One of the central problems in this program is the well-known arbitrariness in choosing a binary operation for implication. To clarify what properties are required to obtain the generalized transfer principle, we introduce a class of binary operations extending the implication on Boolean logic, called generalized implications, including even nonpolynomially definable operations. We study the properties of those operations in detail and show that all of them admit the generalized transfer principle. Moreover, we determine all the polynomially definable operations for which the generalized transfer principle holds. This result allows us to abandon the Sasaki arrow originally assumed for Takeuti’s model and leads to a much more flexible approach to quantum set theory.
言語 en
内容記述タイプ Abstract
出版者
言語 en
出版者 Cambridge University Press
言語
言語 eng
資源タイプ
資源タイプresource http://purl.org/coar/resource_type/c_6501
タイプ journal article
出版タイプ
出版タイプ AM
出版タイプResource http://purl.org/coar/version/c_ab4af688f83e57aa
DOI
関連タイプ isVersionOf
識別子タイプ DOI
関連識別子 https://doi.org/10.1017/S1755020317000120
ISSN
収録物識別子タイプ PISSN
収録物識別子 1755-0203
書誌情報 en : The Review of Symbolic Logic

巻 10, 号 4, p. 782-807, 発行日 2017-12
著者版フラグ
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