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Selected Topics in Set Theory: Constructibility
January 2020, ILLC
Coordination: Dr. Yurii Khomskii
Participants:- Teodor Calinoiu
- James Carr
- David de Graaf
- Jonathan Osinski
- Frank Westers
Constructibility
In 1938 Gödel constructed a model of set theory, known as the Constructible Universe L, in which the Axiom of Choice (AC) and the Generalized Continuum Hypothesis (GCH) are satisfied, proving that neither AC nor GCH could be refuted on the basis of ZF. The model L is generally seen as a "minimal model of set theory", and has since been shown to satisfy many other interesting properties. In this project, we cover the basic theory of Gödel's Constructible Universe L and related topics. In particular:- Models of set theory and absoluteness
- Reflection Theorems
- Basic properties of the constructible universe L
- AC in L
- GCH in L
- Potentially additional topics, e.g.: diamond and combinatorial principles, Suslin trees, definable well-order of the reals, regularity properties for projective sets. <\li>
Textbook
We will use the following textbooks:- Kenneth Kunen, Set Theory (2011 edition)
- Kenneth Kunen, An Introduction to Independence Proofs (1980) (an older version of the same textbook but better in some respects).
- Thomas Jech, Set Theory (2000 edition).
A note about the notation in Kunen's textbooks.
Presentations
Date | Time | Who | What | Pages | Where |
Wednesday 7 Jan | 13-15 | All | Preparatory meeting | F1.15 (ILLC Seminar room) |
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Monday 27 Jan | 15-17 | Frank Westers |
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F1.15 (ILLC Seminar room) |
Tuesday 28 Jan | 11-13 | Teodor Calinoiu |
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F1.15 (ILLC Seminar room) |
Tuesday 28 Jan | 14-16 | David de Graaf |
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F1.15 (ILLC Seminar room) |
Wednesday 29 Jan | 10-12 | James Carr |
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F1.15 (ILLC Seminar room) |
Wednesday 29 Jan | 12.30 - 14.30 | Jonathan Osinski |
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F1.15 (ILLC Seminar room) |