Geodesic
A Comment on “ p < t ”
Canadian mathematical bulletin, Tome 52 (2009) no. 2, pp. 303-314

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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 $\text{M}{{\text{A}}_{{{\aleph }_{1}}}}$ (or a weak version of this) holds, then (of course ${{\aleph }_{2}}\,\le \,\mathfrak{p}\,\le \,\mathfrak{t}$ and) $\mathfrak{p}\,=\,\,{{\aleph }_{2}}\,\Rightarrow \,\mathfrak{p}\,=\,\mathfrak{t}$ . The proof is based on a criterion for $\mathfrak{p}\,<\,\mathfrak{t}$ .
DOI : 10.4153/CMB-2009-033-4
Mots-clés : 03E17, 03E05, 03E50 
Shelah, Saharon. A Comment on “ p < t ”. Canadian mathematical bulletin, Tome 52 (2009) no. 2, pp. 303-314. doi: 10.4153/CMB-2009-033-4
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     title = {A {Comment} on {\textquotedblleft} p &lt; t {\textquotedblright}},
     journal = {Canadian mathematical bulletin},
     pages = {303--314},
     year = {2009},
     volume = {52},
     number = {2},
     doi = {10.4153/CMB-2009-033-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-033-4/}
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