Tag: Teoría de Conjuntos

Abstract. This is the last post in the informal series on ordinals. We give von Neumann’s definition, and show how arithmetical operations can be defined on ordinals by using recursion. Finally we give a property of well ordered chains of subsets of ${\mathbb N}$ that is not shared by ordinary chains. Ordinales a la von…

Abstract. This is the second post about ordinals. In the first one I discussed well-orders and some countable examples. Now we’ll get an eagle’s view on induction and recursion. Inducción y recursión en conjuntos bien ordenados.    La principal utilidad de los conjuntos bien ordenados es que para ellos valen los principios de inducción y de…

Abstract. This is the first post of a series concerning ordinals. I start by motivating their need by means of Cantor-Bendixson derivative, and then develop some of the basic concepts (induction, recursion, arithmetic). Comenzaré discutiendo una operación sobre los subconjuntos de un espacio topológico. Es en algún sentido dual a la clausura, porque en vez…