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日時：10月26日(金) 15:30〜 場所：名古屋大学大学院情報学研究科棟2階206室

講演者：宮元 忠敏(南山大学) タイトル：A note on a countable fast function, its forcing axiom, and a weak tail club guessing アブストラクト： The countable fast function poset is strongly sigma-closed but does not have a usual chain condition. It forces a closed and cofinal subset of the second uncountable cardinal.

Therefore its forcing axiom that takes care of appropriate number of dense sets kills a weak tail club guessing. This weak club guessing is a consequence of a tiny fragment of GCH. We discuss a consistency of the forcing axiom together with CH. We use an Aspero-Mota type iterated forcing with countable symmetric systems of sigma-closed uncountabe elementary substructres of relevant expanding relational structures on a fixed trasitive set universe of a large fragment of set theory. We also dicuss a class of posets that includes this poset and posts with stronger forms of relevant chain condition.

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