Realizations of abstract regular polytopes from a representation theoretic view

Realizations of regular polytopes, II

This note corrects a mistake in the earlier paper with the same title, and gives an example to illustrate the modified theory.

Constructing Regular Ultrafilters from a Model-theoretic Point of View

This paper contributes to the set-theoretic side of understanding Keisler’s order. We consider properties of ultrafilters which affect saturation of unstable theories: the lower cofinality lcf(א0,D) of א0 modulo D, saturation of the minimum unstable theory (the random graph), flexibility, goodness, goodness for equality, and realization of symmetric cuts. We work in ZFC except when noted, as se...

Fuzzy sets form A meta-system-theoretic point of view

Regular polytopes

THE LEFT REGULAR REPRESENTATION OF A COMMUTATIVE SEPARATIVE SEMIGROUP

In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.