How undefinable is truth? (Roman Kossak)

The Logic and Metaphysics Workshop will meet on November 8th from 4:15-6:15 (NY time) via Zoom for a talk by Roman Kossak (CUNY GC).

Title: How undefinable is truth?

Abstract: Almost any set of natural numbers you can think of is first-order definable in the standard model of arithmetic. A notable exception is the set Tr of Gödel numbers of true first-order sentences about addition and multiplication. On the one hand—by Tarski’s undefinability of truth theorem—Tr has no first order definition in the standard model; on the other, it has a straightforward definition in the form of an infinite disjunction of first order formulas. It is definable in a very mild extension of first-order logic. In 1963, Abraham Robinson initiated the study of possible truth assignments for sentences in languages represented in nonstandard models of arithmetic. Such assignments exist, but only in very special models; moreover they are highly non-unique, and—unlike Tr—they are not definable any  reasonable formal system. In the talk, I will explain some model theory behind all that and I will talk about  some recent results in the study of axiomatic theories of truth.

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