Abstract. We give a general method of forcing over categories as a
category-theoretic universal construction which subsumes, on one hand,
all known instances of forcing in set theory, Boolean and Heyting valued
models and sheaf interpretations for both classical and intuitionistic
formal systems; and, on the other hand, constructions of classifying
topoi in topos theory (Grothendieck*s generalization of classifying spaces
considered in algebraic topology, algebraic geometry). The generic
object obtained by forcing is shown to have a clear cohomological meaning.
Furthermore, we show that iterated forcing in set theory, and Grothendieck's
construction of a lax limit of a fibred topos are the same up to Godel's
negative interpretation of classical into intuitionistic logic. This
suqgests possibilities of interapplications between logic, and algebraic
geometry and algebraic topology.
AMS 1980 Mathematics Subject Classification; 03G30, 18B25, 18D30, 03E35,
03F50.
Key words and phrases: classifying topos, geometric theory, universal
model, forcing.
Library of Congress Cataloging in Publication Data
Scedrov, Andrej, 1955-
Forcing and classifying topoi.
(Memoirs of the American Mathematical Society, ISS*T
0065-9266 ; no. 295)
"Volume 48 number 295."
Bibliography: p.
1. Toposes. 2. Categories (Mathematics) 3. Forcing
Obdel theory) I. Title. II, Series: Memoirs of the
American Mathematical Society ; no. 295.
QA3.A57 no. 295 [QA169] 510s [512\55] 83-26644
ISBN 0-8218-2294-2
IV
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