The axiom of infinite choice
Milan R. Tasković · Mathematica Moravica · 2012
In this paper we present the Axiom of Infinite Choice: Given any set P , there exist at least countable choice functions or there exist at least finite choice functions. This paper continues the study of the Axiom of Choice by E. Z e r m e l o [Neuer Beweis für die Möglichkeit einer Wohlordung, Math. Annalen, 65 (1908), 107-128; translated in van Heijenoort 1967, 183-198], and by M. T a s k o v i ć [The axiom of choice, fixed point theorems, and inductive ordered sets, Proc. Amer. Math. Soc., 116 (1992), 897-904]. Fredholm and Leray-Schauder alternatives are two direct consequences of the Axiom of Infinite Choice!.