\(C(WO\), uniformly linearly ordered):  If \(X\) is a well ordered collection of non-empty sets and there is a function \(f\) defined on \(X\) such that for every \(x\in X\), \(f(x)\) is a linear ordering of \(x\), then there is a choice function for \(X\).

\(C(WO,{\Bbb R})\):  Every well ordered family of non-empty subsets of \({\Bbb R}\) has a choice function.

\(C(\aleph_{0},\infty,{\Bbb R})\): Every denumerable family of non-empty sets of reals  has a choice function. Jech [1973b], p 148 prob 10.1.

Every Dedekind finite subset of \({\Bbb R}\) is finite.

(For \(n\in\omega-\{0,1\}\)) If all \(\varSigma^{1}_{n}\), Dedekind finite subsets of \({}^{\omega }\omega\) are finite, then all \(\varPi^1_n\) Dedekind finite subsets of \({}^{\omega} \omega\) are finite.