These proceedings include the papers presented at the logic meeting held at the Research Institute for Mathematical Sciences, Kyoto University, in the summer of 1987. The meeting mainly covered the current research in various areas of mathematical logic and its applications in Japan. Several lectures were also presented by logicians from other countries, who visited Japan in the summer of 1987.

Recursively enumerable sets in models of ?2 collection.- The role of a filter quantifier in set theory.- Syntactical simulation of many-valued logic.- Consistency of Beeson's formal system RPS and some related results.- Elementary properties of a system of fundamental sequences for ?o.- The continuum hypothesis and the theory of the Kleene degrees.- ?1-Collection and the finite injury priority method.- Computational complexity of languages counting random oracles.- Infinitesimal calculus interpreted in infinitary logic.