caa a22 4500 388039779 CHVBK 20180307125018.0 cr unu---uuuuu 161130e199809 xx s 000 0 eng 10.2307/2586725 doi S0022481200014729 pii (NATIONALLICENCE)cambridge-10.2307/2586725 Ideals over ω and cardinal invariants of the continuum [Elektronische Daten] Let P be any one of the following combinatorial properties: weak P-pointness, weak (semi-) Q-pointness, weak (semi-)selectivity, ω-closedness. We deal with the following two questions: (1) What is the least cardinal k such that there exists an ideal with k many generators that does not have the property P? (2) Can one extend every ideal with the property P to a prime ideal with the property P? Copyright © Association for Symbolic Logic 1998 Matet P. Mathematiques, Universite de Caen, 14032 Caen Cedex, France E-mail: matet@math.unicaen.fr Pawlikowski J. Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland E-mail: pawlikow@math.uni.wroc.pl The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 1040-1054 0022-4812 63:3<1040 1998 63 JSL https://doi.org/10.2307/2586725 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586725 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Matet P. Mathematiques, Universite de Caen, 14032 Caen Cedex, France E-mail: matet@math.unicaen.fr NATIONALLICENCE 700 1- Pawlikowski J. Instytut Matematyczny, Uniwersytet Wrocławski, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland E-mail: pawlikow@math.uni.wroc.pl NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 1040-1054 0022-4812 63:3<1040 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge