Almost reconstructing infinite,rayless graphs

We show that for every infinite, rayless graph G the following holds. If G is hypomorphic to H then G is isomorphic to an induced subgraph of G. This proves a conjecture of R. Halin for the class of infinite, rayless graphs and partly extends a result of Bondy and Hemminger. The proof makes use of the structure theory for rayless graphs which was developed by the author in a previous paper.