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Athar Abdul-Quader

Mathematical Logic / Models of Arithmetic

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Decidability and Definability

January 15, 2019January 15, 2019 ~ Athar ~ Leave a comment

This post is an extension of the previous one; I want to address Tarski’s Undefinability Theorem using computability-theoretic methods. Continue reading →

Arithmetic, Self-Reference and Truth

January 13, 2019January 13, 2019 ~ Athar ~ Leave a comment

There is a remarkable theorem in mathematical logic that “Truth is not definable”. This is known as Tarski’s Undefinability Theorem. This result (along with Gödel’s Incompleteness Theorems) has fascinated me ever since I learned about it. This theorem (in a sense) shows us the limits of the ability to study truth within a given formal system. Continue reading →

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