The Bolzano-Weierstrass theorem in generalised analysis
Merlin Carl, Lorenzo Galeotti, Benedikt Löwe · UvA-DARE (University of Amsterdam) · 2018
Let κ be an uncountable regular cardinal with κ<κ= κ. We consider two totally ordered fields κ–ℝ and ℝκ, due to Sikorski and the second author, respectively, that serve as the κ-analogues of the real line and consider generalisations of the Bolzano-Weierstrass theorem for them, showing that for ℝκ, the weak κ-Bolzano-Weierstrass theorem is closely related to the tree property of κ.