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Theorem

Tarski's Undefinability Theorem

Logic and Foundations

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and formal semantics. Informally, the theorem states that arithmetical truth cannot be defined in arithmetic. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Statement
No sufficiently strong formal system can define its own arithmetical truth predicate within itself; informally, arithmetical truth cannot be defined in arithmetic, and more generally truth in a sufficiently rich interpreted language's own standard model cannot be defined inside that same language. 1
Proof Year
1933 1
Connections

In Branch

Sources
1. Tarski's undefinability theorem (Wikipedia)
Wikimedia Foundation
  • Introduction, opening sentence, informal-statement clause
    Informally, the theorem states that "arithmetical truth cannot be defined in arithmetic".
  • Introduction, opening sentence, 1933 attribution clause
    Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics.
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