“Reifying Dynamical Algebra”
Mercoledì 8 Giugno 2022, ore 16:30 - Aula 2AB40 - Ingo Blechschmidt (Università di Augsburg)
Commutative algebra embraces plentiful elegant but abstract proofs. Even for concrete statements, the proofs often appeal to transfinite methods like the axiom of choice or the law of excluded middle.
Following Hilbert’s call, we should work to elucidate how these abstract proofs can be recast in more concrete, computational terms, regarding abstract proofs as intriguing guiding templates for formulating concrete proofs. One such technique for making computational sense of abstract proofs is dynamical algebra, going back to the work of Dominique Duval and her coauthors in 1980’s.
The talk will first present this technique with an illustrative example. Then we will report on joint work with Peter Schuster how to reify dynamical algebra using formal metatheorems of categorical logic, supplying a firm foundation to dynamical algebra. This reification is unlocked by a certain pointfree fractal space, the space of enumerations of a given set. This space allows us to apply methods for countable sets to uncountable sets.