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Recently one of the oldest open problems in set theory about the cardinal invariants of the continuum (i.e the question of whether $\mathfrak{p}=\mathfrak{t}$) was solved by Shelah and Malliaris (see "Cofinality spectrum theorems in model theory, set theory, and general topology").

Can anyone explain the main idea of the above proof.

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I believe it is published. You should look it up and read it. – Monroe Eskew Oct 20 '13 at 5:05
Monroe, sometimes it's useful to get some rough idea of what's going on in the paper and which ideas and techniques are involved in the proof, without having to deeply study the whole paper (which can be very time consuming, considering the fact that it's a Shelah paper). As there are no shorter presentations of the main ideas of the paper (I even asked Saharon to discuss that paper in his seminar, but he preferred to discuss other results), I believe that many people would benefit from a more accessible presentation of some of the main ideas in the paper. – Haim Oct 20 '13 at 22:23
Juris Steprans circulated some notes on this last year at the Fields Institute. These notes were helpful in that they emphasized the set-theoretic content of the proof and pushed the model theory to the background. Perhaps you can contact him? – Todd Eisworth Oct 21 '13 at 13:22

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