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 higherorder logic induced by the topos.  

Question 2: Since, by the ________, a formula F→G is provably true if and only if G is provable from F, it follows that [F]≤[G] if and only if F≼G.  

Question 3: Endow L with a preorder ≼ by defining F≼G if G is an (intuitionist) ________ of F, that is, if G is provable from F.  

Question 4: In this case, the element A → B is the interior of the union of A^{c} and B, where A^{c} denotes the complement of the ________ A.  

Question 5: Then ∼ is an ________; we write H/F for the quotient set.  

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

Question 7: A bounded lattice H is a Heyting algebra if and only if all mappings ƒ_{a} are the lower adjoint of a monotone ________.  

Question 8: Every topology provides a complete Heyting algebra in the form of its ________ lattice.  

Question 9: Given two Heyting algebras H_{1} and H_{2} and a mapping ƒ : H_{1} → H_{2}, we say that ƒ is a ________ of Heyting algebras if, for any elements x and y in H_{1}, we have:  

Question 10: The Lindenbaum algebra of propositional ________ is a Heyting algebra.  

