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Journal of Applied Analysis

Editor-in-Chief: Liczberski, Piotr / Ciesielski, Krzysztof

Managing Editor: Gajek, Leslaw

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Non-Cohen Oracle C.C.C.

S. Shelah12

1The Hebrew University of Jerusalem, Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel. e-mail:

2Department of Mathematics, Hill Center — Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA

Citation Information: Journal of Applied Analysis. Volume 12, Issue 1, Pages 1–17, ISSN (Online) 1869-6082, ISSN (Print) 1425-6908, DOI: https://doi.org/10.1515/JAA.2006.1, June 2010

Publication History

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The oracle c.c.c. is closely related to Cohen forcing. During an iteration we can “omit a type”; i.e. preserve “the intersection of a given family of Borel sets of reals is empty” provided that Cohen forcing satisfies it. We generalize this to other cases. In Section 1 we replace Cohen by “nicely” definable c.c.c., do the parallel of the oracle c.c.c. and end with a criterion for extracting a subforcing (not a complete subforcing, ) of a given nicely one and satisfying the oracle.

Key words and phrases.: 03E35; 03E17

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