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Heyting algebra: Quiz

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Question 1: The global elements of the subobject classifier Ω of an ________ form a Heyting algebra; it is the Heyting algebra of truth values of the intuitionistic higher-order logic induced by the topos.
Category (mathematics)Category theorySheaf (mathematics)Topos

Question 2: Since, by the ________, a formula FG is provably true if and only if G is provable from F, it follows that [F]≤[G] if and only if F≼G.
First-order logicMathematical logicDeduction theoremPropositional calculus

Question 3: Endow L with a preorder ≼ by defining FG if G is an (intuitionist) ________ of F, that is, if G is provable from F.
AristotleWillard Van Orman QuineLogical consequenceBertrand Russell

Question 4: In this case, the element AB is the interior of the union of Ac and B, where Ac denotes the complement of the ________ A.
Metric spaceOpen setClosed setTopological space

Question 5: Then ∼ is an ________; we write H/F for the quotient set.
Equivalence relationGroup (mathematics)Group actionBinary relation

Question 6: Heyting algebras arise as models of ________, a logic in which the law of excluded middle does not in general hold.
Mathematical logicPropositional calculusFirst-order logicIntuitionistic logic

Question 7: A bounded lattice H is a Heyting algebra if and only if all mappings ƒa are the lower adjoint of a monotone ________.
Lattice (order)Adjoint functorsGalois connectionOrder theory

Question 8: Every topology provides a complete Heyting algebra in the form of its ________ lattice.
Open setMetric spaceClosed setTopological space

Question 9: Given two Heyting algebras H1 and H2 and a mapping ƒ : H1H2, we say that ƒ is a ________ of Heyting algebras if, for any elements x and y in H1, we have:
Group (mathematics)HomomorphismMorphismCategory theory

Question 10: The Lindenbaum algebra of propositional ________ is a Heyting algebra.
Propositional calculusIntuitionistic logicFirst-order logicMathematical logic







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