Paul Cohen's method of forcing, together with Saul Kripke's related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set ...

Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

This is a preview. Log in through your library . Abstract Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special ...

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It has taken nearly four years, but mathematicians are finally starting to comprehend a mammoth proof that could revolutionise our understanding of the deep nature of numbers. Mathematicians were ...

It is a mathematical epic five years in the making. In 2012, Shinichi Mochizuki at Kyoto University in Japan produced a proof of a long standing problem called the ABC conjecture, but no one could ...