On Kripke’s proof of Kripke completeness (Melvin Fitting)

The Logic and Metaphysics Workshop will meet on March 13th from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 9205) for a talk by Melvin Fitting (CUNY).

Title: On Kripke’s proof of Kripke completeness

Abstract: Saul Kripke announced his possible world semantics in 1959, and published his proof of axiomatic completeness for the standard modal logics of the time in 1963.  It is very unlike the standard completeness proof used today, which involves a Lindenbaum/Henkin construction and produces canonical models.  Kripke’s proof involved tableaus, in a format that is difficult to follow, and uses tableau construction algorithms that are complex and somewhat error prone to describe. I will first discuss Kripke’s proof, then the historical origins of the modern version.  Then I will show that completeness, proved Kripke style, could actually have been done in the Lindenbaum/Henkin way, thus simplifying things considerably.  None of this is new but, with the parts collected together it is an interesting story. “In my end is my beginning”.

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