Free sequences in P(omega)/fin

0508629 - MÚ 2020 RIV DE eng J - Journal Article
Chodounský, David - Fischer, V. - Grebík, Jan
Free sequences in P(omega)/fin.
Archive for Mathematical Logic. Roč. 58, 7-8 (2019), s. 1035-1051. ISSN 0933-5846. E-ISSN 1432-0665
R&D Projects: GA ČR GF15-34700L; GA ČR GF17-33849L
Institutional support: RVO:67985840
Keywords : dense independent system * maximal free sequence * party forcing
OECD category: Pure mathematics
Impact factor: 0.485, year: 2019
Method of publishing: Limited access
http://dx.doi.org/10.1007/s00153-019-00675-w

We investigate maximal free sequences in the Boolean algebra P(ω) / fin , as defined by Monk (Comment Math Univ Carol 52(4):593–610, 2011). We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted f. Answering a question of Monk, we demonstrate the consistency of ω 1 = i= f< u= ω 2 . In fact, this consistency is demonstrated in the model of Shelah for i< u (Shelah in Arch Math Log 31(6):433–443, 1992). Our paper provides a streamlined and mostly self contained presentation of this construction.
Permanent Link: http://hdl.handle.net/11104/0299484