% Homework Exercises due 15 October

### Questions about identity and functors ###

70. Do Bostock's problem 8.1.3, at the end of the Bostock reading on identity.

71. Show that $Fab \models \forall x(x=a \cond Fxb)$. (This is Sider's problem 5.1a.)

72. Do Sider's problem 5.3, on p. 111.

73. Do Sider's problem 5.4, on p. 113.

### Questions about descriptions ###

74. Do Sider's problem 5.5, on p. 117. (There's a hint on p. 270.)

75. Do Sider's problem 5.7, on p. 119.

76. What are some differences between the complex, functor-using term $successor~of~y$, and the description $\desc x(y=successor~of~x)$? You can assume the domain of quantification is $\N$.

### Questions about multisorted logics and fancier quantifiers ###

77. What is a multisorted logic? Why do Gamut discuss multisorted logics and restricted quantification in the same place?

78. What are the differences between (a) our original quantifiers $\forall$ and $\exists$, (b) restricted quantifiers, and (c) generalized quantifiers?

### Questions about multivalued logic ###

79. What is a multivalued logic? What does $\Gamma \models \phi$ mean when working with a multivalued logic? What does it mean to call one or more truth-values "designated"?

80. Do Sider's problem 3.7, on p. 79. (There's a hint on p. 268.)

### Questions about free logic ###

81. What is a universally free logic? (Sider calls it an inclusive free logic.)

82. Do Sider's problem 5.14, on p. 132.

83. Do Sider's problem 5.15, also on p. 132.

84. Point out at least two major differences between Sider's semantics for free logic and Bostock's.