A variant of Mathias forcing that preserves ACA(0)

作者：Dorais Francois G^*

来源：Archive for Mathematical Logic, 2012, 51(7-8): 751-780.

DOI：10.1007/s00153-012-0297-4

• Mathias forcing
• Second-order arithmetic
• Cohesive sets
• F-sigma ideals

We present and analyze -Mathias forcing, which is similar but tamer than Mathias forcing. In particular, we show that this forcing preserves certain weak subsystems of second-order arithmetic such as and , whereas Mathias forcing does not. We also show that the needed reals for -Mathias forcing (in the sense of Blass in Ann Pure Appl Logic 109(1-2):77-88, 2001) are just the computable reals, as opposed to the hyperarithmetic reals for Mathias forcing.

• 出版日期2012-11