This semester, the course on Walks on Ordinals runs Thursdays, 13--16, building 105, room 4. Here are the weekly lecture notes:

Notes by A. Rinot (English) | Notes by R. Shalev (Hebrew) | Topics |
---|---|---|

Lecture #1 | Lecture #1 | The rudimentaries of walks, the first concatenation lemma, rho_2 and the associated w1-tree |

Lecture #2 | Lecture #2 | The Lambda function and the second concatenation lemma. T(rho_2) is an Aronszajn tree |

Lecture #3 | Lecture #3 | T(rho_2) is isomorphic to a cohrent and special Aronszajn tree |

Lecture #4 | Lecture #4 | rho_1 and its associated coherent Aronszajn tree. The injective variation, and R-embeddability of the two |

Lecture #5 | Lecture #5 | T(rho_1) could be nonspecial, and an initial study of abstract rho funtions |

Lecture #6 | Lecture #6 | The class LO_I, Countryman lines, and initial classification of uncountable linear orders |

Lecture #7 | Lecture #7 | The lexicographic ordering of T(rho_1) is a Countryman line. The partition tree of a Countryman line is an Aronszajn tree. |

Lecture #8 | Lecture #8 | Productivity of the chain condition, L-space and S-space. Pr0 and Pr1. |

Lecture #9 | Lecture #9 | Rotiman's theorem, Galvin's Theorem, and towards Todorcevic's theorem. |

Lecture #10 | Complicated colroings at w1. | |

Lecture #11 | Complicated colroings at higher cardinals. In particular, Pr1(w2,w2,w) holds in ZFC. |

P.s.

The Set Theory seminar runs Thursdays, 10--12, building 604, room 103.