----------------------------------------------------- Kobe Colloquium on Logic, Statistics and Informatics: ----------------------------------------------------- 以下の講演を予定しております．奮ってご参加ください．

------------------------------------------------------------------------- 日時: 2018/04/18 (水) 16.00 - 17:30 場所: 神戸大学六甲台第2キャンパス自然科学総合研究棟3号館421室

講演者 Professor Philip Welch (University of Bristol) 講演題目: Global Reflection Principles

交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」 行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ． http://www.kobe-u.ac.jp/guid/access/rokko/rokkodai-dai2.html

連絡先：渕野 昌 [email protected] --------- Abstract: --------- This talk is based on a paper with Leon Horsten in a recent J.of Phil. and a talk in the Harvard EFI series.

We reflect on the ineffability of the Cantorian Absolute. If this is done in the style of Levy and Montague in a first order manner, or Bernays using second or higher order methods this has only resulted in principles that can justify large cardinals that are `intra-constructible', that is they do not contradict the assumption that V, the universe of sets of mathematical discourse, is Gödel's universe of constructible sets, namely L. Peter Koellner has advanced reasons that this style of reflection will only have this rather limited strength. However set theorists would dearly like to have much stronger axioms of infinity. We propose a widened `Global Reflection Principle' that is based on a view of sets and Cantorian absolute infinities that delivers a proper class of Woodin cardinals (and more). A mereological view of classes is used to differentiate between sets and classes. Once allied to a wider view of structural reflection, stronger conclusions are thus possible. -------------------------------------------------------------------------