MATH 0050
Logic
Course Description
In this course, we will aim to introduce a language for
(first order predicate) mathematical logic and study the interplay between the
notions of 'truth' and 'provability' in the propositional and first order
predicate 'versions' of logic. We will then aim to study computability, via
register machines, recursive functions and coding, and try to use these concepts
to show that first order predicate logic is undecidable.
TOPICS
Language:
Description and construction of a formal language for first order
predicate logic.
Propositional logic:
A study of the semantic and syntactic aspects of propositional logic, including
the semantic tableaux method, and a description of the completeness theorem for
propositional logic and of some of its consequences.
Predicate logic:
A study of the semantic and syntactic aspects of first order predicate logic,
including examples of first order languages and theories, and a description of
the completeness theorem for first order predicate logic and of some of its
consequences.
Computability:
An introduction to recursive partial functions and, via the notion of register
machines, to computable partial functions, and a description of the halting
problem.
Isidoros Strouthos