Logic Symposia Hakone 1979 1980 : Proceedings of Conferences Held in Hakone Japan March 21–24 1979 and February 4–7 1980 Various kinds of Aronszajn tree with no subtree of a different kind On set theories in toposes A representation for Spector second order classes in computation theories on two types Precipitousness of the ideal of thin sets on a measurable cardinal Axiom systems of nonstandard set theory Semi formal finitist proof of the transfinite induction in an initial segment of Cantors second number class On the length of proofs in a formal system of recursive arithmetic Homogeneous formulas and definability theorems Boolean valued combinatorics Undecidability of extensions of the monadic first order theory of successor and two dimensional finite automata Sections and envelopes of type 2 objects Heyting valued universes of intuitionistic set theory Independence of a problem in elementary analysis from set theory Intuitionistic theories and toposes The Hahn Banach theorem and a restricted inductive definition.