Potential infinite models and ontologically neutral logic

Journal of Philosophical Logic 30 (1):79-96 (2001)
The paper begins with a more carefully stated version of ontologically neutral (ON) logic, originally introduced in (Hailperin, 1997). A non-infinitistic semantics which includes a definition of potential infinite validity follows. It is shown, without appeal to the actual infinite, that this notion provides a necessary and sufficient condition for provability in ON logic.
Keywords ontologically neutral logic  potential infinite model  potential infinite validity  generalized tautology
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DOI 10.1023/A:1017576005382
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Jean Van Heijenoort (ed.) (1967). From Frege to Gödel. Cambridge, Harvard University Press.

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