PHIL 320 Chapter 5 Problem Set
Chapter 5
Textbook 5.1
Design an abacus machine for computing the difference function defined by letting
x y = x y if y < x, and = 0 otherwise.
2
1
e
e
This abacus machine starts with x in register 1 and y in regi
PHIL 320 Chapter 13 Problem Set
Chapter 14
Textbook 14.1
Show that:
(a) secures if and only if is unsatisfiable.
Preliminaries: and are finite sets, but result extends to infinite sets. Suppose =cfw_C1, . , Cm
and =cfw_D1, . , Dn. Write ~ for the set o
PHIL 320 Chapter 6 Problem Set
Chapter 6
Textbook 6.1
Let f be a two-place recursive total function. Show the following functions are also recursive:
a) g(x, y) = f(y, x)
!
!
, = (! , , ! , )
b) h(x) = f(x, x)
!
!
() = (! (), ! )
c) k17(x) = f(17, x)
PHIL 320 Chapter 7 Problem Set
Chapter 7
Textbook 7.1
Let R be a two-place primitive recursive. Show that the following relations are also primitive
recursive:
The diagonal of R, given by D(x) R (x, x)
If R is a two-place relation, then its characteris
PHIL 320 Chapter 12 Problem Set
Chapter 12
Textbook 12.1
By the spectrum of a sentence C (or set of sentences ) is meant the set of all positive integers n
such that C (or ) has a finite model with a domain having exactly n elements. Consider a
languag
PHIL 320 Chapter 13 Problem Set
Chapter 13
Textbook 13.2
Show that if is a satisfiable set of sentences, x F(x) a sentence of the language of , and c a
constant not in the language of , then cfw_x F(x)F(c) is satisfiable.
According to the question, we
PHIL 320 Chapter 10 Extra Questions
Chapter 10
Extra Question 1
Let L be the language cfw_a, b, P, R, f and let M be the following interpretation: M is the natural
numbers N, aM = 0, bM = 2, PM(m) iff m is even, RM(m, n) iff n = km for some integer k (
PHIL 320 Chapter 9 Problem Set
Chapter 9
Textbook 9.2
Consider (9) (12) of at the beginning of the chapter, and give an alternative to the genealogical
interpretation that makes (9) true, (10) false, (11) true, and (12) false.
(9) xy (Pyx v Qyx) Ryx)
(
PHIL 320 Chapter 8 Problem Set
Chapter 8
Textbook 8.1
We proved Theorem 8.2 for one-place functions. For two-place (or many-place) functions, the
only difference in the proof would occur right at the beginning, in defining the function strt.
What is th
PHIL 320 Chapter 10 Problem Set
Chapter 10
Textbook 10.2
Show that yx R (x, y) implies xy R (x, y).
According to definition from satisfiability and unsatisfiability, if is unsatisfiable, then
implies D for any D and is unsatisfiable if no interpretati