Kreisel's categoricity argument holds that second-order Peano Arithmetic is categorical, uniquely determining the standard model up to isomorphism despite incompleteness results applying to its first-order fragments.

?Rate how convincing each reason is below to see the overall strength.

No one has weighed in yet. Be the first to share reasons for or against this statement.

First-order fragments(the weaker systems to which incompleteness applies): Simpler versions of a formal system that can only talk about individual objects, not about sets or properties of those objects.
Incompleteness results(as used in mathematical logic): Mathematical theorems proving that in any logical system complex enough to describe math, there will always be true statements that the system cannot prove to be true.
Kreisel(as a historical figure in logic and philosophy of mathematics): Georg Kreisel (1923–2015), a mathematical logician who studied how mathematical reasoning works and whether we can be certain about mathematical truths.
Second-order Peano Arithmetic(the mathematical system being discussed): A formal system for describing the natural numbers (0, 1, 2, 3...) that is more powerful than the basic first-order version because it can quantify over sets and properties, not just individual numbers.

Based on where you are in your exploration