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Mathematical logic: Quiz


Question 1: [1] The field includes both the mathematical study of ________ and the applications of formal logic to other areas of mathematics.

Question 2: The use of infinitesimals, and the very definition of function, came into question in analysis, as pathological examples such as Weierstrass' nowhere-________ continuous function were discovered.
CalculusDerivativeDifferential calculusIntegral

Question 3: The ________ between proofs and programs relates to proof theory, especially intuitionistic logic.
Lambda calculusType theoryFunctional programmingCurry–Howard correspondence

Question 4: proof theory and ________ (considered as parts of a single area).
Constructivism (mathematics)Intuitionistic logicLogicMathematical logic

Question 5: In addition to the independence of the ________, established by Nikolai Lobachevsky in 1826 (Lobachevsky 1840), mathematicians discovered that certain theorems taken for granted by Euclid were not in fact provable from his axioms.
AlhazenParallel postulateGeometryNon-Euclidean geometry

Question 6: Beginning in 1935, a group of prominent mathematicians collaborated under the pseudonym ________ to publish a series of encyclopedic mathematics texts.
Nicolas BourbakiGeometryNumber theoryAlexander Grothendieck

Question 7: His early results developed the theory of ________ and proved that the reals and the natural numbers have different cardinalities (Cantor 1874).
Set theoryCardinal numberCardinalityGeorg Cantor

Question 8: Large cardinals are ________ with particular properties so strong that the existence of such cardinals cannot be proved in ZFC.
Georg CantorNatural numberCardinal numberOrdinal number

Question 9: An early proponent of predicativism was ________, who showed it is possible to develop a large part of real analysis using only predicative methods (Weyl 1918).
Hermann WeylKurt GödelDavid HilbertGeorg Cantor

Question 10: Gödel used the completeness theorem to prove the compactness theorem, demonstrating the finitary nature of first-order ________.
Logical consequenceBertrand RussellAristotleWillard Van Orman Quine


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