Forcing a countable structure to belong to the ground model |
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| Authors: | Itay Kaplan Saharon Shelah |
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| Institution: | 1. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem, Israel;2. Department of Mathematics, Hill Center‐Busch Campus, Rutgers, The State University of New Jersey, 110 Frelinghuysen Road, Piscataway, NJ, United States of America |
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| Abstract: | Suppose that P is a forcing notion, L is a language (in  ),  a P‐name such that  “ is a countable L‐structure”. In the product  , there are names  such that for any generic filter  over  ,  and  . Zapletal asked whether or not  implies that there is some  such that  . We answer this question negatively and discuss related issues. |
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