Many different covering numbers of Yorioka%26apos;s ideals

作者：Osuga Noboru^*; Kamo Shizuo

来源：Archive for Mathematical Logic, 2014, 53(1-2): 43-56.

DOI：10.1007/s00153-013-0354-7

• Null ideal
• Finite support iteration
• Preservation
• Covering number
• Slalom

For , let be the minimal number of functions (or slaloms with width 1) to catch every functions below b in infinitely many positions. In this paper, by using the technique of forcing, we construct a generic model in which there are many coefficients with pairwise different values. In particular, under the assumption that a weakly inaccessible cardinal exists, we can construct a generic model in which there are continuum many coefficients with pairwise different values. In conjunction with these results, we give a generic model in which there are many Yorioka%26apos;s ideals with pairwise different covering numbers.

• 出版日期2014-2