A generalization of Goodstein's theorem: interpolation by polynomial functions of distributive lattices

Details A generalization of Goodstein's theorem: interpolation by polynomial functions of distributive lattices A generalization of Goodstein's theorem: interpolation by polynomial functions of distributive lattices

2011-10-03

arxiv.org/abs/1110.0321v1

Mathematics

Rings and Algebras

12 pages

Scientific paper

We consider the problem of interpolating functions partially defined over a distributive lattice, by means of lattice polynomial functions. Goodstein's theorem solves a particular instance of this interpolation problem on a distributive lattice L with least and greatest elements 0 and 1, resp.: Given an n-ary partial function f over L, defined on all 0-1 tuples, f can be extended to a lattice polynomial function p over L if and only if f is monotone; in this case, the interpolating polynomial p is unique. We extend Goodstein's theorem to a wider class of n-ary partial functions f over a distributive lattice L, not necessarily bounded, where the domain of f is a cuboid of the form D={a1,b1}x...x{an,bn} with ai

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