This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Godel's previously unpublished 1972 1975 conversations with Sue Toledo, along with an appreciation of the same by...
This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal ...
The logician Kurt Godel (1906 1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Godel's work on the foundations and philosophy of mathematics. Their essays explore almost every...
The logician Kurt Godel (1906 1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, am...