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Arnold Beckmann: Consistency of equational theories and the separation problem for bounded arithmetic
Abstract: The separation problem for bounded arithmetic is one of the most important problems in the area due to its tight connections to the question whether computational complexity classes can be separated, the Millennium problem whether P equals NP or not being the most well-known one. Well studied candidates for separating theories of bounded arithmetic are consistency statements of formal theories, building on Kurt Goedel's famous incompleteness theorems. The most promising consistency statements are given by those of certain equational theories. In our talk, we will review the results on consistency of equational theories in the context of the separation problem for bounded arithmetic. We explain the progress that has been made over recent years to advance this problem, and state the research programme that has resulted from it.
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