Logic Semantics with the Potential Infinite

History and Philosophy of Logic 31 (2):145-159 (2011)
Abstract
A form of quantification logic referred to by the author in earlier papers as being 'ontologically neutral' still made use of the actual infinite in its semantics. Here it is shown that one can have, if one desires, a formal logic that refers in its semantics only to the potential infinite. Included are two new quantifiers generalizing the sentential connectives, equivalence and non-equivalence. There are thus new avenues opening up for exploration in both quantification logic and semantics of the infinite
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    Theodore Hailperin (1997). Ontologically Neutral Logic. History and Philosophy of Logic 18 (4):185-200.
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