{'fraction_non_alphanumeric': 0.020599250936329586, 'fraction_numerical': 0.003745318352059925, 'mean_word_length': 3.9537037037037037, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The basis problem for CCC posets

Given a family Σ of forcing notions a subfamily Σ0 of Σ is called a basis provided for every P ∈ Σ there is Q ∈ Σ0 such that forcing with P adds a generic for Q. We investigate the problem of finding a small basis for the class of nonatomic ccc partial orderings. Prikry conjectured that it is consistent that {C,R} forms such a basis, where C is Cohen forcing and R is random real forcing. We survey what is known about this problem and present some new results. Finally we list some open questions.