Math 570: Mathematical Logic
Fall Semester 2009
Prof. Ward Henson
Monday, November 2, 2009
Problem Set 4 Due in class Monday, November 9, 2009
There are four problems (25 points each) and you should do all of them.
To earn full credit requires a careful w
silvain.rideau@berkeley.edu
www.normalesup.org/~srideau/eng
Silvain Rideau
1091 Evans
Homework 1
Due September 10th
Problem 1 (Tautologies) :
We have to do truth tables:
1.
A
0
1
0
1
B
0
0
1
1
[A B]
1
0
1
1
[A B] A]
0
0
0
1
2.
A
0
1
0
1
0
1
0
1
B
0
0
1
1
silvain.rideau@berkeley.edu
www.normalesup.org/~srideau/eng
Silvain Rideau
1091 Evans
Homework 2
Due September 17th
Problem 1 :
Let P = cfw_X1 , X2 , X3 , X4 , X5 , X6 .
n
1. Show that there are at most 302 formulas of height n (this is a very rough estim
silvain.rideau@berkeley.edu
www.normalesup.org/~srideau/eng
Silvain Rideau
1091 Evans
Homework 1
Due September 10th
Problem 1 (Tautologies) :
Prove that the following formulas are tautologies:
1. [A B] A] B];
2. [A B] [C A].
Prove that the following formu
Elements of Mathematical Logic
Michael Meyling
May 24, 2013
2
The source for this document can be found here:
http:/www.qedeq.org/0_04_07/doc/math/qedeq_logic_v1.xml
Copyright by the authors. All rights reserved.
If you have any questions, suggestions or
Copyright c 19982013 by Stephen G. Simpson
Mathematical Logic
Stephen G. Simpson
October 17, 2013
Department of Mathematics
The Pennsylvania State University
University Park, State College PA 16802
http:/www.math.psu.edu/simpson/
This is a set of lecture
Math 570: Mathematical Logic
Fall Semester 2009
Prof. Ward Henson
Friday, September 11, 2009
Problem Set 1 Due in class Friday, September 18, 2009
There are four problems (25 points each) and you should do all of them. To
earn full credit requires a caref
Math 570: Mathematical Logic
Fall Semester 2009
Prof. Ward Henson
Monday, October 12, 2009
Problem Set 3 Due in class Monday, October 19, 2009
There are four problems (25 points each) and you should do all of them.
To earn full credit requires a careful w
2.5
MATH 570 Homework 2
1 Answer to Problem 1.
Proof We shall show that for any Lterm t(a:), tA(n) is bounded by |tln for
n E N, where It! denotes the length oft as a word in L. Then clearly tA(n) < 2"
for large enough n. We show this by induction on
Whe
Math 570: Mathematical Logic
Fall Semester 2009
Prof. Ward Henson
Friday, September 25, 2009
Problem Set 2 Due in class Friday, October 2, 2009
There are four problems (25 points each) and you should do all of them. To
earn full credit requires a careful
Math 570: Mathematical Logic
Fall Semester 2009
Prof. Ward Henson
Monday, November 30, 2009
Problem Set 5 Due in class Monday, December 7, 2009
There are four problems (25 points each) and you should do all of them.
To earn full credit requires a careful
PROBLEM SET 3
Exercise (3.1). Let L have just a constant symbol c, a unary relation symbol U,
a unary function symbol f , and suppose that E l- U fc, and that f does not occur
in the sentences of 2. Then 2 l- Vchsc.
g
Proof. We prove the contrapositiv
silvain.rideau@berkeley.edu
www.normalesup.org/~srideau/eng
Silvain Rideau
1091 Evans
Homework 2
Due September 17th
Problem 1 :
1. Let an = Fn . Then a0 = F0 = P = 6 and an+1 = Fn+1 = Fn + cfw_ Fn cfw_[1 2 ] i
Fn and cfw_, , = 2an + 4a2n 5a2n .
Let us