We solve a problem of Friedman by showing the existence of a logic stronger than first-order logic even for countable models, but still satisfying the general compactness theorem, assuming e.g. the ...

We give a completeness theorem for a logic with probability quantifiers which is equivalent to the logics described in a recent survey paper of Keisler [K]. This result improves on the completeness ...

Logic and geometric representations constitute an interdisciplinary framework that merges formal logical systems with spatial and diagrammatic structures. This field encompasses the study of classical ...

Shalosh B. Ekhad, the co-author of several papers in respected mathematics journals, has been known to prove with a single, succinct utterance theorems and identities that previously required pages of ...

When Aristotle and his predecessors devised their theories of logic and mathematics, they came up with the so-called Law of the Excluded Middle, which states that every proposition must either be true ...