A Comment on ``$mathfrak{p} < mathfrak{t}$'

[摘要] Dealing with the cardinal invariants ${mathfrak p}$ and${mathfrak t}$ of the continuum, we prove that${mathfrak m}={mathfrak p} = aleph_2 Rightarrow {mathfrak t} =aleph_2$.In other words, if ${f MA}_{aleph_1}$ (or a weak version ofthis) holds, then (of course $aleph_2le {mathfrak p}le{mathfrak t}$ and) ${mathfrak p}=aleph_2 Rightarrow{mathfrak p}={mathfrak t}$. The proof is based on a criterionfor ${mathfrak p}<{mathfrak t}$.

[学科分类] 数学（综合）

[关键词] Hamel basis;additive;Hamel functions