STATE
UNIVERSITY COLLEGE AT BUFFALO
Department
of Mathematics
Request
for Course
I. Number
and title of course
MAT 431 - Mathematical Logic
II. Reasons
for addition to the present curricula
A. The course, an extension of
MAT 270. will consist of topics in mathematical logic not covered in courses
presently offered.
B. The course should enable the
student to better appreciate the axiomatic method in mathematics.
C. The course provides a study of formal systems in
contrast to informal systems which is the usual way topics in all other
mathematics courses are presented.
D. The course should help prepare the
student for more formally structured graduate mathematics courses.
E. While other courses may
emphasize skills and knowledge in special areas of mathematics, this course
allows the student to understand the abstract nature and structure of all of
mathematics.
III. Major objectives of the course
A. To acquaint the student with a
basic knowledge of mathematical logic.
B. To help the student better
understand the precise roles of set theory and quantification logic in
mathematics in providing a uniform language and basis for all of mathematics.
C. To develop the students'
understanding and appreciation of the axiomatic method, formal and informal
systems.
IV. Topical
outline
A. Propositional logic
1. Validity and valid
consequence
2. Deducibility in a
formal system
3. Completeness theorems
B. Quantification logic
1. Validity and valid
consequence
2. Deducibility
3. Completeness theorems
b. Other meta theorems
a.
Derived rules
b.
Premex forms
c.
Generalized completeness results
d.
Compactness
5. Applications to
a.
Satisfiability and consistency
b.
Isomorphism and categoricity
c.
Decidability
6. Theories with equality
a.
Normal models
b.
Generalized Lovenheim‑Skolem theorems
C. First order formal theories
1. Group theory
2. Number theory
3. Fields
4. First order geometry
and algebra
D.
Informal theories in the context of set theory
1. Set theory
2. Group theory
3. Number structures
V. Bibliography,
texts, and readings
Christian, P. Introduction
to Logic and Sets New York: Blaisdell
Publishing Co., 1965.
Church, A. Introduction to Mathematical Logic Princeton:
Princeton University Press, 1956.
Copi, I. Introduction to Logic New York: The
Macmillan Co., 1961.
Copi, I. Symbolic Logic New York: The
Macmillan Co., 1965.
Curry, H. Foundations of Mathematical Logic New
York: McGraw‑Hill
Cc., 1963.
Halmos, P.R. Lectures on Boolean Algebra Princeton
: D. Van Nostrand
co., 1963.
Kleene, S.C. Introduction to Metamathematics Princeton:
B. Van Nostrand Co., 1952.
Kneebone, G. Mathematical Logic and the
Foundations of Mathematics
Princeton: D. Van Nostrand Co., 1963.
torndon, B. Notes on Logic Princeton: 0. Van
Nostrand Co., 1966.
Bosscr, J. _Logic for Mathematicians New York:
McGraw‑Hill Co., 1953.
Rosser, 3. and A. Turguette. Many‑valued
Logics New York:
Humanities Press, 1952.
Suppes, P., and S. Hills. First Course in
Mathematical Logic
Boston: Ginn and Co., 1957.
Stoll, B. Set Theory and its Logic San
Francisco: W. H. Freeman
& Co., 1963.
Tarski, A. Introduction to Logic and to the
Methodology of
Deduction Sciences Fair Lawn: Oxford
University Press, 1946.
VI. Presentation
and evaluation
Lectures, discussions,
assigned readings and problems,
written examinations.
VII. Prerequisites
MAT 270 and MAT 202
VIII. Credit
Three
semester hours
IX. Statement
of approval
This course proposal was
examined in accord with recommended
procedures and was approved
by the Department of Mathematics
on February 16, 1967.
I. Catalog
description
MAT 431 ‑ MATHEMATICAL
LOGIC ‑ Validity, deducibility, and completeness in propositional and
predicate logics; first order formal theories and informal theories in the
context of set theory.
Classification: Elective
Prerequisites: MAT 202 and MAT 270
Credit: Three
semester hours ‑ three class hours
XI. Statement
of qualifications of faculty who will teach course.
NAME PREPARATION EXPERIENCE
Barr, Jack Course
work completed for 5 years
Ph.D., at Univ. of Maryland
Blaeuer, David M.A.
Univ. of Wisconsin 1
years
Trautman, Dorothy M.S.,
SUC at Buffalo 5
years
34 semester hours beyond Master
Wiesen, Richard
M.S., Syracuse University
6 years
45 semester hours beyond Masters