# Model theory: Quiz

Question 1: This is a very efficient way to define most classes of ________, because there is also the concept of σ-homomorphism, which correctly specializes to the usual notions of homomorphism for groups, semigroups, magmas and rings.
Algebraic structureRing (mathematics)Group (mathematics)Vector space

Question 2: Model theory is usually concerned with ________, and many important results (such as the completeness and compactness theorems) fail in second-order logic or other alternatives.
QuantificationFirst-order logicAlfred TarskiMathematical logic

Question 3: Model theory has close ties to ________ and universal algebra.
MathematicsAlgebraAlgebraic structureVector space

Question 4: While model theory is generally considered a part of mathematical logic, universal algebra, which grew out of ________'s (1898) work on abstract algebra, is part of algebra.
AristotleWillard Van Orman QuineBertrand RussellAlfred North Whitehead

Question 5: In first-order logic all infinite cardinals look the same to a language which is ________.
Set (mathematics)Cardinal numberGeorg CantorCountable set

Question 6: Whereas universal algebra provides the ________ for a signature, logic provides the syntax.
SemanticsFormal semanticsLinguisticsPragmatics

Question 7: In the context of ________ the analogous statement is trivial, since every proof can have only a finite number of antecedents used in the proof.
Mathematical logicLogicFirst-order logicProof theory

Question 8: Hodges, Wilfrid (1997), A shorter model theory, Cambridge: ________, ISBN 978-0-521-58713-6
Authorized King James VersionCambridge University PressOxford University PressEngland

Question 9: ________ (which is expressed in a countable language) has a countable model; this is known as Skolem's paradox, since there are sentences in set theory which postulate the existence of uncountable sets and yet these sentences are true in our countable model.
Georg CantorModel theoryMathematical logicSet theory

Question 10: Structures are also a part of universal algebra; after all, some ________ such as ordered groups have a binary relation <.
Group (mathematics)Algebraic structureRing (mathematics)Vector space