Forcing a morass with finite side conditions (Infinite Combinatorics and Forcing Theory)

Miyamoto, Tadatoshi

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Forcing a morass with finite side conditions

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We report a forcing poset that forces what we call a morass-type matrix. A condition of the poset is represented by a pair of a finite symmetric system of Aspero-Mota and a finite function from the finite symmetric system into the least uncountable cardinal. The finite function is a restriction of a rank function associated with a type of suitable countable symmetric system that contains the finite symmetric system. It is similar to forcing a club subset of the least uncountable cardinal by finite conditions that accompany finite in-chains of elementary substructures. A difference between these two posets is whether cardinals can be preserved or not. Note that the forced matrix entails not just a club but a simplified morass of D. Velleman.

Journal

RIMS Kokyuroku

RIMS Kokyuroku 2042 88-98, 2017-07

京都大学数理解析研究所