Last modified by jkennedy@helsinki_fi on 2024/03/27 09:58
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1 = Axiomatic set theory, fall 2008 =
2
3 === Lecturer ===
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5 [[PhD Juliette Kennedy>>doc:mathstatHenkilokunta.Kennedy, Juliette]]
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7 === Scope ===
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9 10 sp.
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11 === Type ===
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13 Advanced studies.
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15 === Lectures ===
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17 Weeks 36-42 and 44-50, Monday 16-18 and Wednesday 16-18 in room B322. (% style="color: rgb(255,0,0);" %)**For corrections to Lemma 2.8 page 96 see**(%%):[[http:~~/~~/mat-238.math.helsinki.fi/note.pdf>>url:http://mat-238.math.helsinki.fi/note.pdf||shape="rect"]]
18
19 === Contents ===
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21 After covering the basic axioms, we move on to constructibility and the beginnings of forcing. Our text is Kunen's "Axiomatic Set Theory."
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23 === Prerequisites ===
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25 Students should be familiar with the basic theory of cardinal and ordinal numbers, as set out for example in Enderton's "Elements of Set Theory."
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27 === Course material ===
28
29 ==== Homework. ====
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31 |=(((
32 Week
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34 Exercises
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37 37
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39 Prove Theorem 7.3, 1-6 in detail. Page 43, problems 4,8,9.
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42 38
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44 Prove Theorem 7.18, 1-5, 7.20, 1-6, 10.6, 10.10 in detail. Page 44, problems 10 a-c,15.
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47 39
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49 p.45, 18. Prove: there is a continuous, strictly increasing cofinal function from cf(alpha) to alpha. (An increasing function f is continuous if f(u) = sup(f(z), z<u) for each limit u.) Prove: f is continuous iff f is continuous in the order topology of ordinals. (I.e. the topology generated by open intervals.) NOTE: STUDENTS DO NOT HAVE TO FINISH THESE BY THE TIME THE EXERCISE CLASS MEETS, BUT THE CLASS WILL BE HELD AND THE EXERCISES WILL BE GONE OVER.
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52 40
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54 This week Lauri will review section 14.3 in preparation for chapter 4.
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57 41
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59 Prove lemma 3.5, page 99. Prove Theorem 3.6, page 100. Prove lemma 5.8, page 104. page 107, exercises 1,3.
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62 43
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64 Page 146, 1,2,3.
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67 44
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69 p.131, prove Lemma 6.4 in detail. p.147, 8, 14, 17.
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72 45
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74 The instructor will discuss HOD and prove p.163, 5.
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77 46
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79 p. 182, 19,20,21.
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82 47
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84 p.180, 1,4,5.
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87 48
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89 p.238,A5-A8. Prove lemmas 2.11-18 in detail, p. 190.
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92 49
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94 Prove theorem 4.2 in detail.
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96
97 === [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57247||shape="rect"]] ===
98
99 === Final Exam: Monday, December 15, 12-16, B322. (% style="text-decoration: underline; color: red" %)**NOTE NEW EXAM TIME.**(%%) ===
100
101 === Exercise groups ===
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103 |=(((
104 Group
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106 Day
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108 Time
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110 Place
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112 Instructor
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115 1.
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117 Tue
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119 12 - 14
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121 B312
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123 Lauri Tuomi
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