DOIAbstract
For every n ϵ ω \ {0,1} we introduce the following weak choice principle: nC- <N0 : For every infinite family F of finite sets of size at least n there is an infinite subfamily G⊆F with selection fuction f : G → [⋃G]n such that f (F) ∈ [F]n for all F ∈ G. Moreover, we consider the following choice principle: KWF– : For every infinite family F of finite sets of size at least 2 there is an infinite subfamily G ⊆ F with a Kinna-Wagner selection function. That is, there is a function g : P(⋃G) with ∅ ≠ f (F) ⊂_\ F for every F ∈ G. We will discuss the relations between these two choice principlesand their relations to other well-known weak choice principles. Moreover, we will discuss what happens when we replace F by a linearly order...
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