Author Archives: gentzen

About gentzen

Logic, Logic, and Logic

A subset interpretation (with context morphisms) of the sequent calculus for predicate logic

The previous two posts used the sequent calculus with a subset interpretation: We work with sequents , and interpret the propositions (and ) as subsets of some universe set . We interpret the sequent itself as . While writing the … Continue reading

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Logic without negation and falsehood

In the last post, consideration related to partial functions lead us to present a logic without truth and implication, using the binary minus operation as a dual of implication and substitute for unary negation. But logic without implication and equivalence … Continue reading

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Logic without truth

Pi is wrong! But so what? It is neither new, nor complicated enough to count as real math! And suggestions that  or  might be even better show that it not clear-cut either. I recently invested sufficient energy into some logical questions to … Continue reading

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Learning category theory: a necessary evil?

The end of my last blog post (about isomorphism testing of reversible deterministic finite automata) explained how category theory gave me the idea that the simplified variant of my question about permutation group isomorphism should be easy to solve: The idea to consider … Continue reading

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A canonical labeling technique by Brendan McKay and isomorphism testing of deterministic finite automata

A deterministic finite automaton (DFA) is a 5-tuple, , consisting of a finite set of states a finite set of input symbols a (partial) transition function an initial state a set of accept states An isomorphism between two DFAs and … Continue reading

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On Zeros of a Polynomial in a Finite Grid: the Alon-Furedi bound

Originally posted on Anurag's Math Blog:
My joint paper with Aditya Potukuchi, Pete L. Clark and John R. Schmitt is now up on arXiv: arXiv:1508.06020. This work started a few months back when I emailed Pete and John, pointing out an easy generalization…

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Groupoids

Originally posted on Annoying Precision:
My current top candidate for a mathematical concept that should be and is not (as far as I can tell) consistently taught at the advanced undergraduate / beginning graduate level is the notion of a…

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