Phil 151
Winter 2013
Problem Set # 5 (due February 21, 2013)
1. (Enderton 2.2.1) Show that
(a) cfw_ |= if and only if |= ( ); and
(b) if and only if |= ( ).
2. (Enderton 2.2.2) Show that no one of the following sentences is logically implied
by the other
Phil 151
Winter 2013
Problem Set # 2 (due January 24, 2013)
1.
a. Prove that (A1 A2 ) (A3 (A1 A3 ) is a w.
b. Prove that (A3 A4 ) is not a w.
2. Dene the function s : w N such that s() is the number of symbols in ,
counting multiple occurences of the same
Phil 151
Winter 2013
Problem Set # 7 (due March 8, 2013)
1. (Enderton 2.2.23) Let A be a structure and g a one-to-one function with domain
|A|. Show that there is a unique structure B such that g is an isomorphism
from A onto B.
2. (Enderton 2.4.2) To whi
Phil 151
Winter 2013
Problem Set # 4 (due February 7, 2013)
1. (Enderton 1.7.1) Assume that every nite subset of is satisable. Show that
the same is true of at least one of the sets cfw_ and cfw_. (This is part
of the proof of the compactness theorem, so
Phil 151
Winter 2013
Problem Set # 3 (due January 31, 2013)
1. Suppose , w, prove the following:
a. |= if and only if ( ) is a tautology.
b. if and only if ( ) is a tautology.
2. Let and be ws whose sentence symbols are among A1 , . . . , An . And let <
a
Phil 151
Winter 2013
Problem Set # 6 (due February 28, 2013)
1. (Enderton 2.2.8) Assume that is a set of sentences such that for any sentence
either |= or |= . Assume A |= . Show that for any sentence ,
A |= if and only if |= .
2. (Enderton 2.2.9) Let L
Phil 151
Winter 2013
Problem Set # 8 (due March 14, 2013)
1. (Enderton 2.5.1) (Semantical rule EI) Assume that the constant symbol c does
not occur in , or , and that ; x |= . Show (without using the soundness
c
and completeness theorems) that ; x |= .
2.
Phil 151
Winter 2013
Problem Set # 1 (due January 17, 2013)
1. For each of the following, prove the statement or show that it is false by providing a counterexample.
a. For all sets X ,
X=
P (X ).
b. For all sets X ,
X = P(
X ).
2. For each of the followi