Logical Consequence: Models and Modality

Source abstract

Abstract My long-standing interest in the notion of logical consequence became urgent when I was working on my recent book on higher-order logic (1991). The most common complaint is that second-order logic is out of bounds. as logic, because its consequence relation is not effective. Even though higher order logic is squarely within the prevailing model-theoretic tradition, its set of logical truths is not recursively enumerable-it is not even in the Kleene hierarchy.