743 research outputs found
Proof theory of weak compactness
We show that the existence of a weakly compact cardinal over the
Zermelo-Fraenkel's set theory is proof-theoretically reducible to iterations of
Mostowski collapsings and Mahlo operations
Derived rules for predicative set theory: an application of sheaves
We show how one may establish proof-theoretic results for constructive
Zermelo-Fraenkel set theory, such as the compactness rule for Cantor space and
the Bar Induction rule for Baire space, by constructing sheaf models and using
their preservation properties
On Tarski's fixed point theorem
A concept of abstract inductive definition on a complete lattice is
formulated and studied. As an application, a constructive and predicative
version of Tarski's fixed point theorem is obtained.Comment: Proc. Amer. Math. Soc., to appea
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