Last modified by asaekman@helsinki_fi on 2024/03/27 10:47
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1 = Introduction to continuous logic, fall 2015 =
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6 **Teacher:** [[Åsa Hirvonen>>doc:mathstatHenkilokunta.Hirvonen, Åsa]]
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8 **Scope:** 5 op
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10 **Type:** Advanced studies
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12 **Teaching:**
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14 **Topics: **Continuous logic is a [0,1]-valued generalization of first order logic developed for the study of metric structures such as Banach spaces and operator algebras. This course gives a short introduction to the logic and its models.**
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17 **Prerequisites: **Logic I or Mathematical logic is recommended.**
18 **
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21 === {{toc maxLevel="4" minLevel="2" indent="20px"/}} ===
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23 == News ==
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25 * 18.12. The grading of the course is ready. The grade should show in Oodi soon. For more details, contact the lecturer.
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27 == Teaching schedule ==
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29 Weeks 44-50, Monday 10-12 and Thursday 14-16 in room B120. In additon, two hours of exercise classes per week.
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31 == Exams ==
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33 Course exam on Wednesday 16.12. at 12.00-14.30 in one of the auditoriums in Exactum.
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35 == Course material ==
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37 As course material we will use the following survey article:
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39 I. Ben Yaacov, A. Berenstein, C.W. Henson, A. Usvyatsov, //Model theory for metric structures,// in: Model Theory with Applications to Algebra and Analysis, Vol. II, Z. Chatzidakis et al. (eds.), London Math. Soc. Lecture Note Ser. 350, Cambfidge Univ. Press, Cambridge, 2008. Available via C. Ward Henson's webpage [[www.math.uiuc.edu/~~~~henson/cfo/mtfms.pdf>>url:http://www.math.uiuc.edu/~~henson/cfo/mtfms.pdf||shape="rect"]]
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41 == [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57072||shape="rect"]] ==
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44 (% style="color: rgb(96,96,96);" %)Did you forget to register? (%%)[[What to do?>>url:https://wiki.helsinki.fi/display/mathstatOpiskelu/Kysymys4||style="text-decoration: underline;" shape="rect"]]
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46 == Exercises ==
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48 === Assignments ===
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50 * [[Set 1>>attach:cfo_h1.pdf]] (for 6.11.) exercise added 2.11. (note: some uniform continuity needs to be assumed in 1)
51 * [[Set 2>>attach:cfo_h2.pdf]]
52 * [[Set 3>>attach:cfo_h3.pdf]] (note: there was an error in exercise 3.2, it is now corrected)
53 * [[Set 4>>attach:cfo_h4.pdf]] (note: in 5, M needs to be non-compact)
54 * [[Set 5>>attach:cfo_h5.pdf]]
55 * [[Set 6>>attach:cfo_h6.pdf]]
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57 === Exercise classes ===
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59 |=(((
60 Group
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62 Day
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64 Time
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68 Instructor
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73 Friday
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75 10-12
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77 C123
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79 Åsa Hirvonen
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81
82 == Logbook ==
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84 26.10. Formulas
85 29.10. Systems of connectives
86 2.11. Semantics
87 5.11. logical equivalence, logical distance, conditions, theories
88 9.11. example: the theory of probability algebras; elementary embeddings and substructures
89 12.11. Tarski-Vaught Test; filters, ultrafilters and D-limits
90 16.11. Ultraproducts
91 19.11. The Fundamental Theorem of Ultraproducts
92 23.11. Compactness
93 26.11. Saturation
94 30.11. more on saturation
95 3.12. Implications; Types and the logic topology
96 7.12. The d-metric on types
97 10.12. Short glimpse on definability and distance predicates
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99 == Course feedback ==
100
101 Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]].