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Showing posts from September, 2019

Not a Knot II

This post belongs to LoPSE popularization (#pop) series written both in English and in Polish.


In a previous post we presented the background needed to follow Paula Teijeiro in her Not a knot. Now we're ready to move to the paper discussed during the seminar, which raises two key points. First, it is possible to provide a syntactic characterization of Knot. This is done in a proof system which is a bit different from what one might see in an intro to logic class, but there are no clear reasons not to call this a proof-theoretic characterization.
Since the notion of a conservative extension doesn't help here, the question arises as to whether there is a similar criterion in the vicinity that would allow to establish that Knot in some sense hasn't been properly introduced. One strategy, that Teijeiro investigates, is to define a new notion: that of a preservative extension. Roughly speaking, the idea here is that preservative extensions …