This conference will be a sequel to the 1st Conference on the core model induction and hod mice that was held in Münster (FRB), July 19 -- August 06, 2010, to the 2nd Conference on the core model induction and hod mice that was held in Münster (FRG), August 08 -- 19, 2011, to the AIM Workshop on Descriptive Inner Model Theory, held in Palo Alto (CA), June 02 -- 06, 2014, to the Conference on Descriptive Inner Model Theory, held in Berkeley (CA) June 09 -- 13, 2014 to the 3rd Münster Conference on inner model theory, the core model induction, and hod mice that was held in Münster (FRG), July 20 -- 31, 2015, as well as to the 1st Irvine conference on descriptive inner model theory and hod mice that was held in Irvine (CA), July 18 -- 29, 2016.

Once more, this conference will draw together researchers and advanced students with an interest in inner model theory, in order to communicate and further explore this recent work. There will be courses and single talks.

We will meet Monday--Friday, with 2 hours of lecture in the morning and 2 hours of lecture in the early afternoon. This will leave ample time for problem sessions, informal seminars, and other interactions in the late afternoons and evenings.

The conference will take place at the Department of Mathematics and Computer Science, Univ. of Muenster, Seminar room N2 (1st week) and lecture hall M6 (2nd and 3rd week).

The conference organizers gratefully acknowledge financial support from the American NSF (through Grigor Sargsyan and John Steel), from the Marianne and Dr. Horst Kiesow-Stiftung, Frankfurt a.M., and from the German logic society, DVMLG.

Mon, July 17 | Tue, July 18 | Wed, July 19 | Thu, July 20 | Fri, July 21 | |

9:30--10:45 | Schlutzenberg: Tutorial I part 1 | Wilson: Tutorial II part 1 | Zhu: Tutorial I part 3 | Zeman: Tutorial III part 2 | Goldberg 1 |

11:15--12:30 | Schlutzenberg: Tutorial I part 2 | Wilson: Tutorial II part 2 | Zhu: Tutorial I part 4 | Zeman: Tutorial III part 3 | Goldberg 2 |

14:30--15:45 | Zeman: Tutorial III part 1 | Ben-Neria 1 | Wilson: Tutorial II part 3 | Schindler 1 | Zeman: Tutorial III part 4 |

16:15--17:30 | "Paradoxical sets" seminar: Beriashvili | Ben-Neria 2 | Wilson: Tutorial II part 4 | Schindler 2 | Ben-Neria 3 |

17:30--∞ | -- | Problems and Discussions | -- | Problems and Discussions | free |

Mon, July 24 | Tue, July 25 | Wed, July 26 | Thu, July 27 | Fri, July 28 | |

9:30--10:45 | Trang | Sargsyan I, 1 | Jackson | Castiblanco | Steel: Tutorial IV part 1 |

11:15--12:30 | Zeman: Tutorial III part 5 | Sargsyan I, 2 | Zeman: Tutorial III part 6 | Miedzianowski | Steel: Tutorial IV part 2 |

14:30--15:45 | Adolf 1 | Uhlenbrock | Zeman: Tutorial III part 7 | Aguilera | Sargsyan II, 1 |

16:15--17:30 | Adolf 2 | Fernandes | Steel | Blue | Sargsyan II, 2 |

17:30--∞ | Problems and Discussions | Problems and Discussions | Problems and Diskussions | Problems and Discussions | free |

Mon, July 31 | Tue, Aug 01 | |

9:30--10:45 | Steel: Tutorial IV part 3 | Schlutzenberg 1 |

11:15--12:30 | Steel: Tutorial IV part 4 | Schlutzenberg 2 |

14:30--15:45 | Sargsyan | free |

16:45--17:30 | Wilson: Tutorial II part 5 | free |

17:30--∞ | Problems and Discussions | Problems and Discussions |

- Dominik Adolf:
**A derived model satisfying Θ ≥ θ**. Abstract: See title. This is joint work with G. Sargsyan. Notes by rds: Adolf, part 1, Adolf, part 2_{ω2} - Juan Aguilera:
**Making Δ**. Abstract: We prove some results on games of length ω_{1}Determined Again_{1}that strengthen provably-Δ_{1}determinacy. This is joint work with Douglas Blue. Notes by rds: Aguilera, - Omer Ben-Neria:
**The failure of diamond principle at large cardinals**. In pursuit of an understanding of the relations between compactness and approximation principles, we address the following question: To what extent do compactness principles assert the existence of a diamond sequence? It is well known that a cardinal κ which satisfies a sufficiently strong compactness assumption must also carry a diamond sequence. However, other results have shown that certain weak large cardinal assumptions are consistent with the failure of the full diamond principle. We will discuss this gap and describe some known and recent results. Notes by rds: Ben-Neria, part 1, Ben-Neria, part 2, Ben-Neria, part 3. - Doug Blue and Martin Zeman:
**Tutorial III on ◻**. Parts 1, 2, 3, 4, and 5 (Zeman): the Schimmerling-Zeman characterization of square in short extender models. Part 6 (Blue): the difficulties for square in plus-one premice. Notes by Stefan Miedzianowski: Zeman, part 1, Zeman, part 2, Zeman, part 3, Zeman, part 4, Zeman, part 5. Slides: Blue._{κ}in mice, long extender mice, and least-branch hod mice - Fabiana Castiblanco:
**The ordinal u**. Abstract: Under the existence of sharps for reals the second uniform indiscernible can be defined as u_{2}and a thin Δ^{1}_{3}equivalence relation_{2}= sup{ ω_{1}^{+L[x]}: x a real }. Suppose that P is Sacks, Mathias, Silver, Miller or Laver forcing. In this talk we will see that if every real has a sharp then u_{2}^{V}= u_{2}^{VP}and, in fact, P does not add any new equivalence class to the Δ^{1}_{3}-thin equivalence relation defined by xEy iff ω_{1}^{+L[x]}= ω_{1}^{+L[y]}. File: Castiblanco, - Gabriel Fernandes:
**Cardinal arithmetic and Woodin cardinals**. Abstract: If ω_{3}< cf (κ) < κ, for all α < κ we have ℶ_{α}(α) ∈ κ and S = {α < κ | 2^{α}> α^{+}} is stationary and co stainary, then there is a mouse M such that M∩OR = κ and M |= ∀α∃δ > α(δ is a Woodin cardinal). This is joint work with Ralf Schindler. Notes by rds: Fernandes - Gabriel Goldberg:
**Supercompact cardinals and the Mitchell order**. Abstract: We introduce a general comparison principle for ultrafilters, the Ultrapower Axiom, that along with GCH implies that the Mitchell order is linear on supercompactness measures. For example, the result applies to the Woodin and Neeman-Steel models at the finite levels of supercompactness, even though in these models many supercompactness measures, and even normal measures, do not appear on the sequence. Notes by rds: Goldberg, part 1, Goldberg, part 2. Notes by Stefan Miedzianowski: Goldberg, part 3. - Steve Jackson:
**Some new partition and non-partition results from AD**. Abstract: Assuming AD, we identify the exact exponent partition properties the successor and double successor of regular limit Suslin cardinals have, and some related questions. This is joint work with Apter, Blass, and Lowe. File: Jackson. - Stefan Miedzianowski:
**Inner Model Theoretic Geology**. Abstract: We analyze the mantle of the least inner model with a strong cardinal which itself is a limit of Woodin cardinals. This is joint work with Ralf Schindler. Notes by rds: Miedzianowski. - Grigor Sargsyan I:
**PFA implies a model of LSA**. Abstract: Exactly what is in the title. Joint work with Nam Trang. Notes by rds: Sargsyan, part 1, Sargsyan, part 2 - Grigor Sargsyan II:
**Strategy Representation Hypotheses below non-domestic hod mice**. Abstract: We show that under AD^{+}if there is non-domestic hod mouse then every set of reals is Wadge reducible to a code of an iteration strategy. Notes by rds: Sargsyan. - Ralf Schindler:
**Varsovian models with more Woodin cardinals**. We report on joint work with Grigor Sargsyan. Varsovian models, II (1st part), Varsovian models, II (2nd part), Varsovian models, II (3rd part), Varsovian models, II (4th part), Varsovian models, II (5th part), Varsovian models, II (6th part), Varsovian models, II (appendix), Varsovian models, II (appendix 2). Notes by Stefan Miedzianowski: Schindler, part 1 and 2. - Farmer Schlutzenberg and Yizheng Zhu:
**Tutorial I on the derived model theorem**. File: Schlutzenberg, notes by rds: Zhu, part 1 and 2. - Farmer Schlutzenberg:
**Semiscales constructed from mice**. Abstract: In approximately 1999, Neeman announced a construction of scales directly from mice, avoiding determinacy arguments. His work remains unpublished. We will describe a new construction which produces semiscales directly from mice. It yields, for example, Semiscale(Π^{1}_{3}). Notes by rds: Schlutzenberg, part 1, Schlutzenberg, part 2. - John Steel:
**Tutorial IV on lbr hod pairs and local HOD computation**: propagating HPC past inductive-like classes, and models of LSA and stronger things from lbr hod pairs. Notes by rds: Steel, part 1, Steel, part 2. Slides: Steel, part 2. - Nam Trang:
**An outline of the core model induction**Abstract: We give a brief and nontechnical introduction to the core model induction. We describe how the core model induction works, what type of problems one can tackle with the core model induction, and the current state of the subject. Notes by rds: Trang, part 1, Trang, part 2 - Sandra Uhlenbrock:
**HOD in inner models with finitely many Woodin cardinals**. Abstract: We analyze HOD in the inner model M_{n}(x,g) for reals x of sufficiently high Turing degree and a suitable generic g. This is joint work with Grigor Sargsyan. Notes by rds: Uhlenbrock - Trevor Wilson:
**Martin's closure operation and scales on local Π**. We develop some basic properties of the "closure operation" introduced by Martin that maps a pointclass S to S = { A : for every countable σ there is some A' in S such that A ∩ σ = A' ∩ σ }. Applying this operation to a local version of the pointclass OD gives an "envelope" pointclass that precisely describes the complexity of scales for the corresponding local version of Π^{2}_{1}sets^{2}_{1}. Applications include (1) the Kechris-Woodin determinacy transfer theorem, which together with results of Steel establishes the pattern of scales in L(R), and (2) Woodin's result that the intersection of divergent models of AD^{+}satisfies "every set of reals is Suslin." Notes by rds: Wilson, part 1, Wilson, part 2, Wilson, part 3, Wilson, part 4, Wilson, part 5.

Dominik Adolf (Münster) | ₰ D | |

Juan P. Aguilera (TU Vienna) | ₰ K | |

Omer Ben-Neria (UCLA) | ₰ K | |

Mariam Beriashvili (Tbilisi) | July 16--? | Europa Haus |

Douglas Blue (Harvard) | ₰ J | |

Fabiana Castiblanco (Münster) | ||

Justin Cavitt (Harvard) | ₰ G | |

Gabriel Fernandes (Münster) | ||

Elliot Glazer (Rutgers) | ₰ G | |

Gabriel Goldberg (Harvard) | July 16--Aug 05 (?) | |

Steve Jackson (Texas) | July 23--Aug 01 | Handwerkskammer |

Ronald Jensen (Berlin) | July 29--Aug 06 | Hotel am Schloßpark |

Martin Köberl (Rutgers) | ₰ G | |

Stefan Miedzianowski (Münster) | ||

Bill Mitchell (Gainesville) | July 17--Aug 05 | Hotel Bakenhof + Hotel am Schloßpark |

Dan Saattrup Nielsen (Bristol) | ₰ K | |

Menachem Magidor (Jerusalem) | July 21--Aug 06 | Europa Haus |

Grigor Sargsyan (Rutgers) | July 16--Aug 08 | Germania Campus |

Ralf Schindler (Münster) | ||

Farmer Schlutzenberg (Münster) | ||

Benjamin Siskind (Berkeley) | ₰ J | |

John Steel (Berkeley) | July 14--Aug 08 | Hotel am Schloßpark + Humboldt Haus |

Nam Trang (UC Irvine) | July 18--? | Germania Campus |

Sandra Uhlenbrock (Vienna) | ||

Trevor Wilson (Miami Univ., Oxford OH) | ||

Shi Xianghui (Beijing) | ||

Yizheng Zhu (Münster) | ||

Martin Zeman (UC Irvine) | July 16--Aug 04 | Germania Campus |