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A FORMALISM FOR SOME CLASS OF FORCING NOTIONS
Author(s) -
Koszmider Piotr,
Koszmider P.
Publication year - 1992
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19920380140
Subject(s) - forcing (mathematics) , countable set , mathematics , formalism (music) , class (philosophy) , pure mathematics , construct (python library) , discrete mathematics , computer science , mathematical analysis , artificial intelligence , art , musical , visual arts , programming language
Abstract We introduce a class of forcing notions, called forcing notions of type S , which contains among other Sacks forcing, Prikry‐Silver forcing and their iterations and products with countable supports. We construct and investigate some formalism suitable for this forcing notions, which allows all standard tricks for iterations or products with countable supports of Sacks forcing. On the other hand it does not involve internal combinatorial structure of conditions of iterations or products. We prove that the class of forcing notions of type S is closed under products and certain iterations with countable supports.