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A variant of Mathias forcing that preserves
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) are just the computable reals, as opposed to the hyperarithmetic reals
for Mathias forcing