A Problem Course in Mathematical Logic

A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints.


Parts I and II, Propositional Logic and First-Order Logic respectively, cover the basics of these topics through the Soundness, Completeness, and Compactness Theorems, plus a little on applications of the Compactness Theorem. They could be used for a one-term course on these subjects. Part III, Computability, covers the basics of computability using Turing machines and recursive functions; it could be used as the basis of a one-term course. Part IV, Incompleteness, is concerned with proving the Gödel Incompleteness Theorems. With the omission of some topics from Part III which are not needed to prove the results in Part IV, Parts III and IV could be used for a one-term course for students who know the contents of Part II already.


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

Book Details

Author(s): Stefan Bilaniuk
Format(s): PDF, PostScript
File size: 726 KB
Number of pages: 126
Link: Download.

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