Jacob Lurie: Higher Topos Theory is published by Princeton University Press and copyrighted, © 2009, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing...

A complete lattice L is constructively completely distributive CCD L if the sup map de ned on down closed subobjects has a left adjoint It was known that in boolean toposes CCD L is equivalent to CCD L We show here that the latter property for all L su ciently for characterizes boolean toposes Research partially supported by grants from NSERC Canada Diagrams typeset using catmac Introduction Th...

In this paper it is shown that the ordered structure of the Dedekind real numbers is effectively homogeneous in any topos with natural numbers object. This result is obtained within the framework of local set theory.