What does Gödel's second incompleteness theorem state?
The system can prove its inconsistency
The system cannot prove its consistency
The system is complete
The system is incomplete
Answer
Gödel's second incompleteness theorem states that any consistent system of axioms whose theorems can be listed by an "effective procedure" (essentially, a computer program) is incomplete. This means that there are statements about the natural numbers that are true, but that are unprovable within the system. Theorem has profound implications for the foundations of mathematics.
The Gödelicious Quiz: Unraveling the Genius of Kurt Gödel
More Questions
What theory could neither the axiom of choice nor the continuum hypothesis be disproved from?
The axiom of choice was opened up for assumption by Gödel's proof. True or False?
Who made important contributions to proof theory by connecting classical logic, intuitionistic logic and modal logic?
When did Kurt Gödel pass away?
In Gödel's time, who were major figures working with logic and set theory to examine the mathematical foundations?
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