Presented By: Logic Seminar - Department of Mathematics
Logic Seminar: The Extension of Post's Lattice to Countable Borel Clones
Ilir Ziba
Given a set of cardinals N and an underlying set X, an N-ary function clone on X is a set of functions f: Xⁿ → X for n ∈ N, which contains all projection functions and is closed under composition. In 1941, Emil Post fully characterized all clones of finite functions f: 2ⁿ → 2 in a lattice famously titled Post’s lattice, ordered by inclusion. In this second seminar on this topic, we will again motivate the two main perspectives towards clones, discuss new results, and briefly touch on the current focus of this project.
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