Abstract

BOGOYA, Johan  and  MONTENEGRO, Carlos. UNA DEBILITACIÓN DEL AXIOMA DE ELECCIÓN PARA EL ÁRBOL BINARIO ESTÁNDAR. Rev.colomb.mat. [online]. 2006, vol.40, n.2, pp.111-117. ISSN 0034-7426.

The axiom of choice says that for any collection of sets (or for any set of sets) X, exists a function f such that f(x) ∈ x for all non empty x ∈ X, i.e. f takes an element in each set of the collection X, such function is called a choice function, it is customary to weak the axiom of choice by putting some extra condition for the set X such that: "X is a n-set collection, meaning that the elements of X are finite sets of size n" or in the other hand, weakening the choice function f by changing the condition f(x) ∈ x by the simpler one Ø 6= f(x) ¢ x, in this last case we say that f is a sellector function. We say that the S_n criterion is true in a model M if all the possible collections of n-sets X in M, have a sellector function. In the present work we exhibit a permutation model of finite support [2, chapter 4] where the S_n criterion fails for all the naturals n of the form 2^k with k natural, and works for the rest of the naturals

Keywords : Logic; models; axiom of choice.

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