# Gödel's incompleteness theorems: Quiz

Question 1: Gödel's incompleteness theorems are two theorems of mathematical logic that state inherent limitations of all but the most trivial ________ for mathematics.
Set theoryKurt GödelGeorg CantorAxiomatic system

Question 2: The incompleteness theorem is closely related to several results about undecidable sets in ________.
Hilary PutnamFirst-order logicComputability theoryMathematical logic

Question 3: Chaitin's theorem states that for any theory that can represent enough arithmetic, there is an upper bound c such that no specific number can be proven in that theory to have ________ greater than c.
Entropy (information theory)Data compressionKolmogorov complexityInformation theory

Question 4: It is similar, for example, to the way English sentences are encoded as sequences (or "strings") of numbers using ________: such a sequence is considered as a single (if potentially very large) number.
Windows-1252ISO/IEC 8859-1Code page 437ASCII

Question 5: In mathematical logic, a theory is a set of sentences expressed in a ________.
Formal grammarFormal languageContext-free grammarRegular language

Question 6: In 1977, Paris and Harrington proved that the Paris-Harrington principle, a version of the Ramsey theorem, is undecidable in the first-order axiomatization of arithmetic called ________, but can be proven to be true in the larger system of second-order arithmetic.
Mathematical logicPeano axiomsKurt GödelFirst-order logic

Question 7: The theorems were proven by Kurt Gödel in 1931, and are important in the ________.
Outline of philosophyAristotlePhilosophy of mathematicsLogic

Question 8: While Gödel's theorem is related to the ________, Chaitin's result is related to Berry's paradox.

Question 9: The ________ is the sentence "This sentence is false." An analysis of the liar sentence shows that it cannot be true (for then, as it asserts, it is false), nor can it be false (for then, it is true).

Question 10: The incompleteness results affect the ________, particularly versions of formalism, which use a single system formal logic to define their principles.
EmpiricismPhilosophy of mathematicsOutline of philosophyAristotle