The Bolzano-Weierstrass Theorem in Generalised Analysis
Merlin Carl, Lorenzo Galeotti, Benedikt Löwe

Abstract:
Abstract. 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.