Foundations of Mathematics Symposium Papers Commemorating the Sixtieth Birthday of Kurt Gödel

Dr. KURT GODEL'S sixtieth birthday (April 28, 1966) and the thirty­ fifth anniversary of the publication of his theorems on undecidability were celebrated during the 75th Anniversary Meeting of the Ohio Ac­ ademy of Science at The Ohio State University, Columbus, on April 22, 1966. The celebration took the form of a Festschrift Symposium on a theme supported by the late Director of The Institute for Advanced Study at Princeton, New Jersey, Dr. J. ROBERT OPPENHEIMER: "Logic, and Its Relations to Mathematics, Natural Science, and Philosophy." The symposium also celebrated the founding of Section L (Mathematical Sciences) of the Ohio Academy of Science. Salutations to Dr. GODEL were followed by the reading of papers by S. F. BARKER, H. B. CURRY, H. RUBIN, G. E. SACKS, and G. TAKEUTI, and by the announcement of in-absentia papers contributed in honor of Dr. GODEL by A. LEVY, B. MELTZER, R. M. SOLOVAY, and E. WETTE. A short discussion of "The II Beyond Godel's I" concluded the session.

Realism as a Philosophy of Mathematics.- The Undecidability of ?K-Conversion.- The Definability of Cardinal Numbers.- The Use of Symbolic Logic in Proving Mathematical Theorems by Means of a Digital Computer.- A New Approach to the Foundations of Probability.- Measure-Theoretic Uniformity.- On the Cardinality of $$ \sum\nolimits_2^1 {} $$ Sets of Reals.- The Universe of Set Theory.- Definition eines (relativ vollständigen) formalen Systems konstruktiver Arithmetik.