The RIMS meeting “Reflection principles and set theory of large cardinals”

will take place from Sept. 9 till Sept. 12 at the Research Institute for

Mathematical Sciences, Kyoto University, Japan. this meeting is organized

by Sakae Fuchino.

#### Guest Speakers

- James Cummings Mini Course on “Large Cardinals and Forcing”
- Stevo Todorčević Combinatorial Reflection Principles

We expect many talks, in particular by junior participants, both from Japan and abroad. people interested in attending should contact Sakae Fuchino. fuchino@diamond.kobe-u.ac.jp

12:10–14:00 Lunch Time

09:00–09:10 | Opening |

09:10–10:10 | James CummingsLarge cardinals and forcing (mini course (1/4)) |

10:30–11:15 | David Asperó Forcing locally definable well-orders of the universe without the GCH [slides] |

11:25–12:10 | Laura Fontanella Large properties at small cardinals |

14:00–14:45 | Michael HrušákGeneric existence of MAD families |

15:10–15:55 | Teruyuki Yorioka Side condition method and the preservation of a tower in ${\cal P}(\omega)$ |

16:10–16:55 | Aleksander Błaszczyk $P_\lambda$-filters and regular embeddings |

**September 10 (Tu)**

09:00–10:00 | James CummingsLarge cardinals and forcing (mini course (2/4)) |

10:30–11:15 | Andrew Brooke-Taylor On cardinal characteristics of large cardinals |

11:25–12:10 | Diego Alejandro Mejía Guzmán Template iterations with non-definable posets |

12:10–13:50 | Lunch Time |

13:50–14:20 | Osvaldo Guzman Namba forcing and set theory of the reals |

14:30–15:00 | Arturo Antonio Martinez Canjar Ideals |

15:20–15:50 | Jonathan Cancino Manriquez Countable irresolvable spaces |

16:00–16:20 | Shohei Tajiri A remark on “Can you take Solovay’s inaccessible away?” |

16:30–17:00 | David Chodounský Some combinatorics in ${\cal P}(\omega)$ [slides] |

**September 11 (We)**

12:00–13:40 Lunch Time

Short talks session:

09:00–10:00 | James CummingsLarge cardinals and forcing (mini course (3/4)) | ||||||||

10:30–12:00 | Stevo Todorčević;Combinatorial Reflection Principles | ||||||||

13:40–14:00 | Vincenzo Dimonte Very Large Cardinals and the failure of GCH |
14:05–14:25 | Luz María García-Ávila A forcing notion related to Hindman’s Theorem (new properties) |
14:30–14:50 | Sakaé Fuchino A proof of the Fodor-type Reflection Principle from the Rado Conjecture [slides] |
14:55–15:15 | Toshimichi Usuba Superdestructibility of superstrong and other large cardinals [preprint] |
15:20–15:40 | Hiroshi Sakai $n$-stationary sets and $\Pi^1_{n-1}$-indescribable cardinals |

**September 12 (Th)**

09:00–10:00 | James CummingsLarge cardinals and forcing (mini course (4/4)) |

10:20–11:05 | Masahiro Shioya A simplified approach to saturated ideals |

11:15–12:00 | Tadatoshi Miyamoto Matrices of isomorphic models and morass-like structures |

12:10–13:40 | Lunch Time |

13:40–14:25 | Ulises Ariet Ramos García Intersection numbers of families of ideals |

14:35–15:20 | Liuzhen Wu $\Delta_1$ definability of the full nonstationary ideal on cardinals |

15:20–15:30 | Closing |