{"id":8065,"date":"2022-03-29T17:58:11","date_gmt":"2022-03-29T12:58:11","guid":{"rendered":"https:\/\/scholarpublishing.org\/sse\/?p=8065"},"modified":"2022-06-02T10:45:35","modified_gmt":"2022-06-02T05:45:35","slug":"eb198","status":"publish","type":"post","link":"https:\/\/scholarpublishing.org\/sse\/eb198\/","title":{"rendered":"Global Set Theory"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"8065\" class=\"elementor elementor-8065\">\r\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7599e364 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7599e364\" data-element_type=\"section\" data-e-type=\"section\">\r\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\r\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7c902baf\" data-id=\"7c902baf\" data-element_type=\"column\" data-e-type=\"column\">\r\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\r\n\t\t\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-5f5ed588 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5f5ed588\" data-element_type=\"section\" data-e-type=\"section\">\r\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\r\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-23861217\" data-id=\"23861217\" data-element_type=\"column\" data-e-type=\"column\">\r\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\r\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b67b76e custom-sub-heading elementor-widget elementor-widget-heading\" data-id=\"b67b76e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Global Set Theory<\/h2>\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t\t<\/div>\r\n\t\t<\/section>\r\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-5fd53447 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5fd53447\" data-element_type=\"section\" data-e-type=\"section\">\r\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\r\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-inner-column elementor-element elementor-element-18733f5a\" data-id=\"18733f5a\" data-element_type=\"column\" data-e-type=\"column\">\r\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\r\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3d4638d7 elementor-widget elementor-widget-heading\" data-id=\"3d4638d7\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t<h6 class=\"elementor-heading-title elementor-size-default\">Satoko Titani<\/h6>\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-42210af6 elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"42210af6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"icon-list.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\r\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\r\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Professor Emeritus, Chubu University, Japan<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t<\/ul>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-1507b901 elementor-icon-list--layout-inline elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"1507b901\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"icon-list.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items elementor-inline-items\">\r\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item elementor-inline-item\">\r\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\"><strong>DOI:<\/strong><\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item elementor-inline-item\">\r\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/doi.org\/10.14738\/eb.198.2021\" target=\"_blank\">\r\n\r\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">https:\/\/doi.org\/10.14738\/eb.198.2021<\/span>\r\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t<\/ul>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-38c50a30 elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"38c50a30\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"icon-list.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\r\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\r\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\"><strong>Keywords:<\/strong><\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\r\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Classical Logic, Logical Axioms, Quantum Physics<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t<\/ul>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-67eaa3d4 custom-text-justify elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"67eaa3d4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"icon-list.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\r\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\r\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\"><strong>Abstract:<\/strong><\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\r\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Our reasoning is based on 2-valued logic. That is, we are convinced that a statement is either true or false. 2-valued logic is said to be the logic of the Absolute. The true (1) and the false (0) are expressions of the degree of truth, and called truth values. Truth values 1 and 0 form a complete Boolean lattice 2 with operations \u2228, \u2227, \u00ac : 2 = \u27e8 {1, 0} : \u2227(and), \u2228 : (or), \u00ac(not) \u27e9 The logic represented by Boolean lattice is called a classical logic. Thus, we accept the law of excluded middle and distributive law as logical axioms. Classical set theory is developed by the classical logic with axioms which characterize \u2018sets\u2019. The whole sets forms the universe of set theory. A model V of the universe of classical set theory is constructed inductively from empty set \u2205 by adding power sets of existing sets repeatedly : V\u03b1 = {u | \u2203\u03b2 \u2208\u03b1(u:V\u03b2 \u21922)}, V = \u222a \u03b1\u2208On V\u03b1 , where subset of V\u03b2 is represented by 2-valued characteristic function, i.e. u \u2282 V\u03b2 def \u21d0\u21d2 u:V\u03b2 \u21922. Mathematics, which is a language of science, is developed in the classical set theory.<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t<\/ul>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-136259b3 elementor-widget elementor-widget-text-editor\" data-id=\"136259b3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t\t\t<!-- References Button -->\n<div class=\"py-3 text-center\"><button class=\"btn btn-lg btn-primary\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapseExample\" aria-expanded=\"false\" aria-controls=\"collapseExample\">\nView References\n<\/button><\/div>\n\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-bd619ae elementor-widget elementor-widget-text-editor\" data-id=\"bd619ae\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t\t\t<div id=\"collapseExample\" class=\"collapse mt-3\"><ol><li>Abor J., Adjasi C.K.D., and Hayford Mac-Clara (2008): \u201cHow Does Foreign Direct Investment Affect the Export Decisions of Firms in Ghana?,\u201d African Development Review, Vol. 20 No. 3, pp. 446-65.<\/li><li>Afxentiou, P.C., and A. 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Titani<\/span>\r\n\t\t\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t<\/ul>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-a349712 dropdown-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"a349712\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\r\n\t\t\t<span class=\"elementor-divider-separator\">\r\n\t\t\t\t\t\t<\/span>\r\n\t\t<\/div>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-c48465c custom-sub-heading elementor-widget elementor-widget-heading\" data-id=\"c48465c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\">License<\/h5>\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-702006b3 elementor-widget elementor-widget-text-editor\" data-id=\"702006b3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t\t\t<p>This work is licensed under a\u00a0<a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\" rel=\"license\">Creative Commons Attribution 4.0 International License<\/a>.<\/p>\t\t\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t<div class=\"elementor-element elementor-element-47d393fa dropdown-divider elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"47d393fa\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\r\n\t\t\t\t<div class=\"elementor-widget-container\">\r\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\r\n\t\t\t<span class=\"elementor-divider-separator\">\r\n\t\t\t\t\t\t<\/span>\r\n\t\t<\/div>\r\n\t\t\t\t\t\t<\/div>\r\n\t\t\t\t<\/div>\r\n\t\t\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t\t<\/div>\r\n\t\t<\/section>\r\n\t\t\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t\t\t\t\t<\/div>\r\n\t\t<\/section>\r\n\t\t\t\t<\/div>\r\n\t\t","protected":false},"excerpt":{"rendered":"<p>Our reasoning is based on 2-valued logic. That is, we are convinced that a statement is either true or false. 2-valued logic is said to be the logic of the Absolute. The true (1) and the false (0) are expressions of the degree of truth, and called truth values. Truth values 1 and 0 form a complete Boolean lattice 2 with operations \u2228, \u2227, \u00ac : 2 = \u27e8 {1, 0} : \u2227(and), \u2228 : (or), \u00ac(not) \u27e9 The logic represented by Boolean lattice is called a classical logic. Thus, we accept the law of excluded middle and distributive law as logical axioms. Classical set theory is developed by the classical logic with axioms which characterize \u2018sets\u2019. The whole sets forms the universe of set theory. A model V of the universe of classical set theory is constructed inductively from empty set \u2205 by adding power sets of existing sets repeatedly : V\u03b1 = {u | \u2203\u03b2 \u2208\u03b1(u:V\u03b2 \u21922)}, V = \u222a \u03b1\u2208On V\u03b1 , where subset of V\u03b2 is represented by 2-valued characteristic function, i.e. u \u2282 V\u03b2 def \u21d0\u21d2 u:V\u03b2 \u21922. Mathematics, which is a language of science, is developed in the classical set theory.<\/p>\n","protected":false},"author":2,"featured_media":8072,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"plain-container","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"disabled","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[2,45,49,60,65,68],"tags":[375,376,377],"class_list":["post-8065","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ebooks","category-earth-sciences","category-engineering","category-mathematics","category-physics","category-social-sciences","tag-classical-logic","tag-logical-axioms","tag-quantum-physics"],"_links":{"self":[{"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/posts\/8065","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/comments?post=8065"}],"version-history":[{"count":24,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/posts\/8065\/revisions"}],"predecessor-version":[{"id":8636,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/posts\/8065\/revisions\/8636"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/media\/8072"}],"wp:attachment":[{"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/media?parent=8065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/categories?post=8065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/scholarpublishing.org\/sse\/wp-json\/wp\/v2\/tags?post=8065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}