Math 486 Homework 1 Notes
Paul Shafer pshafer@math.cornell.edu February 5, 2008
Problem I.1.8a
We are to prove that (Nn , <L ) is a well order. It is reasonably clear that (Nn , <L ) is a linear order, so we need to prove the following: every nonemp
Math 486 Homework 2 Notes
Paul Shafer pshafer@math.cornell.edu February 12, 2008
Problem I.3.3
We show that the proposition has a CNF by using the fact that has a DNF. Let (1,1 1,n1 ) (k,1 1,nk ) be the DNF of , where each i,j is
Math 486 Homework 3 Notes
Paul Shafer pshafer@math.cornell.edu February 19, 2008
Everyone did well this week. I only have a few minor points.
Problem I.5.1
Most of you handled each case by writing, for example, "if V( ) = T then V() = T or V() = T
Math 486 Homework 4 Notes
Paul Shafer pshafer@math.cornell.edu February 26, 2008
Problem I.6.8
We give two proofs that a countable graph is 4-colorable if every finite subgraph is 4-colorable. Proof via Knig's lemma: Let G = ({a0 , a1 , . . . }, E)
Applied Logic
Lecture Notes
07-02-08
1 A Proof Algorithm
A paintbot moves along the nodes of the refutation tree of , painting nodes red or blue according to a specific set of rules. Start. Start at root, in mode , going , with all nodes painted blu
Applied Logic
Lecture Notes
12-02-08
1 Generalized Refutation Trees
Up until this point we were only concerned with validity and provability without hypotheses. We saw that both of these notions were closely related to the existence of consistent fi
Applied Logic
Lecture Notes
19-02-08
1 Equational Logic
A signature is a map : F {0, 1, 2, } where F is a family of distinct symbols. The terms of signature , or simply -terms, are defined by the following rules: Every variable symbol x0, x1, If
Applied Logic
Lecture Notes
22-01-08 The following are brief lecture notes and some additional remarks on the Axiom of Choice. Much of the material can be found in Chapter VI of the text, but it is conveniently gathered here for future reference. The
Applied Logic
Lecture Notes
31-01-08
1 Assertion and Refutation Labellings
The key concept of the lecture is that of the assertion and refutation labellings of the formation tree of a proposition . This is a signed labelling much like the evaluation