Bilanuik S. A Problem Course in Mathematical Logic

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Department of Mathematics Trent University, 1991, -186 pp.

This is a text for a problem-oriented undergraduate course in mathematical logic. It covers the basics of propositional and first-order logic through the Soundness, Completeness, and Compactness Theorems.
Volume II, Computation, covers the basics of computability using Turing machines and recursive functions, the Incompleteness Theorems, and complexity theory through the P and NP. It covers the basics of computability, using Turing machines and recursive functions, and G?del's Incompleteness Theorem, and could be used for a one semester course on these topics. Volume I, Propositional and First- Order Logic, covers the basics of these topics through the Soundness, Completeness, and Compactness Theorems.

Propositional Logic
Language
Truth Assignments
Deductions
Soundness and Completeness
First-Order Logic
Languages
Structures and Models
Deductions
Soundness and Completeness
Applications of Compactness
Computability
Turing Machines
Variations and Simulations
Universal Turing Machines and the Halting Problem
Computable and Non-Computable Functions
Primitive Recursive Functions
Recursive Functions
Incompleteness
Preliminaries
Coding First-Order Logic
Defining Recursive Functions In Arithmetic
The Incompleteness Theorem

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