{"_buckets": {"deposit": "2160aac8-b4ef-4938-ab81-f6f17a818e66"}, "_deposit": {"id": "25738", "owners": [], "pid": {"revision_id": 0, "type": "depid", "value": "25738"}, "status": "published"}, "_oai": {"id": "oai:nagoya.repo.nii.ac.jp:00025738"}, "item_10_biblio_info_6": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2017-12", "bibliographicIssueDateType": "Issued"}, "bibliographicIssueNumber": "4", "bibliographicPageEnd": "807", "bibliographicPageStart": "782", "bibliographicVolumeNumber": "10", "bibliographic_titles": [{"bibliographic_title": "The Review of Symbolic Logic"}]}]}, "item_10_description_4": {"attribute_name": "\u6284\u9332", "attribute_value_mlt": [{"subitem_description": "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\u2013Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti\u2019s 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\u2019s model and leads to a much more flexible approach to quantum set theory.", "subitem_description_type": "Abstract"}]}, "item_10_publisher_32": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "Cambridge University Press"}]}, "item_10_relation_11": {"attribute_name": "DOI", "attribute_value_mlt": [{"subitem_relation_type_id": {"subitem_relation_type_id_text": "https://doi.org/10.1017/S1755020317000120", "subitem_relation_type_select": "DOI"}}]}, "item_10_rights_12": {"attribute_name": "\u6a29\u5229", "attribute_value_mlt": [{"subitem_rights": "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. \u00a9 2017 Cambridge University Press."}]}, "item_10_select_15": {"attribute_name": "\u8457\u8005\u7248\u30d5\u30e9\u30b0", "attribute_value_mlt": [{"subitem_select_item": "author"}]}, "item_10_source_id_7": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "1755-0203", "subitem_source_identifier_type": "ISSN"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "OZAWA, MASANAO"}], "nameIdentifiers": [{"nameIdentifier": "76304", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2018-05-08"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "MO170514_ppt.pdf", "filesize": [{"value": "171.7 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 171700.0, "url": {"label": "MO170514_ppt", "url": "https://nagoya.repo.nii.ac.jp/record/25738/files/MO170514_ppt.pdf"}, "version_id": "c4e219ad-8772-468e-9ef7-24733283604a"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "journal article", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY"}]}, "item_type_id": "10", "owner": "1", "path": ["312/313/314"], "permalink_uri": "http://hdl.handle.net/2237/00027943", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2018-05-08"}, "publish_date": "2018-05-08", "publish_status": "0", "recid": "25738", "relation": {}, "relation_version_is_last": true, "title": ["ORTHOMODULAR-VALUED MODELS FOR QUANTUM SET THEORY"], "weko_shared_id": null}