105 0 obj >> endobj �o�u�SHi�ih� 4/�\$��F�d�}� I\u9�+� 113 0 obj (\376\377\0004\000.\0001\000\040\000F\000o\000u\000n\000d\000a\000t\000i\000o\000n\000\040\000a\000n\000d\000\040\000I\000n\000f\000i\000n\000i\000t\000y) endobj 48 0 obj << /S /GoTo /D (chapter.1) >> Historical Introduction 1 THE BACKGROUND OF SET THEORY Although set theory is recognized to be the cornerstone of the “new” mathematics, there is nothing essentially new in the intuitive idea of a set. endobj >> >> endobj This alone assures the subject of a place prominent in human culture. (\376\377\0002\000.\0003\000\040\000O\000r\000d\000e\000r) 116 0 obj 定理 4.9 （ p.108 ）を参照） 2) ．さらに 1960 年代になると，コーエン (Paul Cohen 1934 {) は，強制法を導入し，これを用いて選択公理と連続体仮説の 集合論の他の公理からの独立性を証明した（ [Cohen 1963,1964] | 定理 4.17 （ p.118 (\376\377\0002\000.\0004\000\040\000S\000i\000n\000g\000l\000e\000t\000o\000n\000s\000\040\000a\000n\000d\000\040\000C\000l\000a\000s\000s\000\040\000P\000a\000i\000r\000s) << /S /GoTo /D (section.4.1) >> The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe important properties of sets, and give examples. /Filter /FlateDecode endobj endobj (\376\377\000I\000n\000d\000e\000x) This is a typical approach to Set Theory, i.e., sets are treated as primitive s of the theory and are not definable in more basic terms. This theory is interesting for two reasons. endobj :M��[�-{=��~�7�nۻ�֎k���ńjoӈb��L��������sS7�ଲBSk��Y����\"�B�M�%.|V;�Kt�5W��4[���lr�&/�Nxk��� ��Y45 5�ǢP�9���u�x����=4�{��o���༺?)������ǿ�0M|w����x���2�()�!��}�TF���%�(�M�ũ\$/"�~����������! 97 0 obj 124 0 obj 93 0 obj endobj '蜁�X��@8E�W�� p��A�i�0����: endobj (\376\377\000I\000n\000t\000r\000o\000d\000u\000c\000t\000i\000o\000n) endobj 14 0 obj endobj %���� 28 0 obj 16 0 obj Copyright © 2020 NWC Books. 85 0 obj << /S /GoTo /D (chapter*.3) >> Introduction to Logic and Set Theory-2013-2014 General Course Notes December 2, 2013 These notes were prepared as an aid to the student. 36 0 obj The major changes in this new edition are the following. stream 52 0 obj 117 0 obj >> endobj (\376\377\0003\000.\0001\000\040\000S\000e\000t\000s) endobj 101 0 obj /Length 479 17 0 obj x��ZKo�6��W�{����iZ��-�[у_s��Կ_J��X2E��>R�,�I��C� Second, every mathemati-cal statement or proof could be cast into formulas within set theory. 125 0 obj 25 0 obj << /S /GoTo /D (section.1.2) >> 33 0 obj << Capital letters represent sets: A, B, C, … b. (\376\377\0005\000.\0002\000\040\000A\000p\000p\000l\000i\000c\000a\000t\000i\000o\000n\000s\000\040\000o\000f\000\040\000t\000h\000e\000\040\000A\000x\000i\000o\000m\000\040\000o\000f\000\040\000C\000h\000o\000i\000c\000e) 33 0 obj 134 0 obj << Intro to Set Theory Sets De nitions (4.1{4.1.1) Subsets De nition: One set is a subset of another if every element of the rst set is also an element of the second. %���� << /S /GoTo /D [133 0 R /FitH ] >> 41 0 obj /Filter /FlateDecode << /S /GoTo /D (section.2.1) >> 133 0 obj << An Introduction to Elementary Set Theory Guram Bezhanishvili and Eachan Landreth 1 Introduction In this project we will learn elementary set theory from the original historical sources by two key gures in the development of set theory, Georg Cantor (1845{1918) and Richard Dedekind (1831{1916). The elements of a set are the objects in a set. << /S /GoTo /D (section.4.5) >> (\376\377\0005\000\040\000A\000x\000i\000o\000m\000\040\000o\000f\000\040\000C\000h\000o\000i\000c\000e) 21 0 obj endobj endobj (\376\377\0003\000.\0005\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000\040\000A\000l\000g\000e\000b\000r\000a) (4) a. 4.7 Embedding mathematics into set theory 4.7.1 Z 4.7.2 Q 4.7.3 R 4.8 Exercises 5. (\376\377\0003\000.\0007\000\040\000M\000a\000p\000s\000\040\000a\000n\000d\000\040\000F\000u\000n\000c\000t\000i\000o\000n\000s) endobj endobj endobj (\376\377\000P\000r\000e\000f\000a\000c\000e) Measure theory 1 x1.1. endobj 73 0 obj (\376\377\0003\000.\0006\000\040\000E\000q\000u\000i\000v\000a\000l\000e\000n\000c\000e\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000s) /Type /Page 56 0 obj (\376\377\0003\000.\0004\000\040\000R\000e\000l\000a\000t\000i\000o\000n\000s) 29 0 obj /Length 166 88 0 obj 104 0 obj An introduction to measure theory Terence Tao Department of Mathematics, UCLA, Los Angeles, CA 90095 E-mail address: tao@math.ucla.edu. endobj 89 0 obj Notation. (\376\377\0002\000.\0006\000\040\000P\000o\000w\000e\000r\000\040\000C\000l\000a\000s\000s\000\040\000B\000u\000i\000l\000d\000i\000n\000g) (\376\377\0004\000\040\000N\000a\000t\000u\000r\000a\000l\000\040\000N\000u\000m\000b\000e\000r\000s) endobj endobj endobj 136 0 obj << n��l�-�?���?���;|��)����X.�g˱���fFz\$���\$������x]/O9B� @.�yz�� ,�Kó��U_��\$p��C��gld.�\$�p\$�Е��cS,� @Mh��[i�^C}��k�a :�7 The set T = {2,3,1} is equal to S because they have the 137 0 obj << endobj endobj 76 0 obj endobj << /S /GoTo /D (section.2.2) >> %PDF-1.4 �'��I�Y��%��/ (\376\377\0003\000.\0003\000\040\000C\000a\000r\000t\000e\000s\000i\000a\000n\000\040\000P\000r\000o\000d\000u\000c\000t) endobj (\376\377\0004\000.\0005\000\040\000R\000e\000c\000u\000r\000s\000i\000o\000n) This document contains the mathematical foundation of set theory. Set theory is very useful as a language for mathematics. Goal is 81 0 obj >> endobj /Resources 134 0 R endobj stream (\376\377\000B\000i\000b\000l\000i\000o\000g\000r\000a\000p\000h\000y) 8 0 obj /D [133 0 R /XYZ 99.895 776.796 null] x��W=o1��.�b��Qtt���>\$\$R�����k{7�/(��۱����c{F�)R(?RA��#�V�[u���O5�)�ԭ��-~W��e� fDȧ�b*��aĔ;|�*ƀ-�056�@~�f)���V�[��Y���h��'�e�>އ�Q8���#�f@Θ�yD�LU���z&x[5Us�k2�A�nҲ�:�-��p endobj 131 0 obj >> 61 0 obj 24 CHAPTER 2. endobj << /S /GoTo /D (chapter*.14) >> endstream Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Two models of set theory 85 6.1 A set model for ZFC 6.2 The constructible universe 6.3 Exercises 7. ?� �3�v��["�%I��U�j��ͥ�9��:�.D�ǷY9�:h��V4o�5 Q~t۰ ���/@ endobj endobj endstream endobj gures in the development of set theory, Georg Cantor (1845{1918) and Richard Dedekind (1831{1916). endobj (\376\377\0001\000\040\000B\000a\000s\000i\000c\000s) 1. 121 0 obj endobj �ӳ�RO�T���K\$o�m޴��H�ݸct���Cv���+`�c=�ʲ�.l�f7H5������t�tl8� /MediaBox [0 0 595.276 841.89] 40 0 obj <> Chapter 0 Introduction Set Theory is the true study of inﬁnity. 112 0 obj endobj 16 0 obj (\376\377\0006\000\040\000C\000o\000n\000t\000i\000n\000u\000u\000m) endobj 135 0 obj << endobj ,: E�XD��c��b��z�}ӛ���z�6�'�MB�;Q�z4�����_��M�����!k ���5�ˉX1χb�\���g�a�\N��\}�1[���� �`C5@����g�M�!��j. 129 0 obj <>/ProcSet[/PDF/Text/ImageC/ImageB/ImageI]>> << /S /GoTo /D (chapter.2) >> endobj (\376\377\0002\000.\0005\000\040\000I\000n\000f\000i\000n\000i\000t\000e\000\040\000B\000o\000o\000l\000e\000a\000n\000\040\000O\000p\000e\000r\000a\000t\000o\000r\000s)