New manuscript on Cook's conjecture

martdowd at martdowd at
Mon Dec 12 14:48:47 EST 2022


I have a new manuscript on Cook's conjecture:
 A Case of Cook's Conjecture

Here's the abstract:
In 1975 Cook conjectured that the representing formulas of the consistency
of PV do not have polynomially bounded extended resolution proofs.
In 2020 the author noted that it is a question of interest, even whether
it is provable in PV from $\Con_{\text PV}$ that such proofs exist.
Here, it is shown that this question has a negative answer.
Some related theorems are proved, and a
discussion given of further research.

I had previously posted
 A Theorem on Cook's Conjecture
This made a conjecture, which is proved in the new manuscript, so I have
deleted the old manuscript.

Martin Dowd

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