I teach Logic II. First lecture: September 9, 08.15-10.00. (See preliminary schedule.) Literature: Tourlakis, George: Lectures in Logic and Set Theory, volume 1: Mathematical Logic. Cambridge University Press, 2003. ISBN: 0 521 75373 2 (hardback).
EXAM INFORMATION: Compulsory exercises (For deadline and instructions, read the exercise sheet!) available, at last:one, two (corrected version 16/10), three,four.
These exercises should be handed in before deadline in order to qualify for the oral exam in December. (See date below.)
ADDITIONAL EXAMS: For those who do fail on the compulsory exercises (or the oral exam), there are two additional oral exams next year, one after Easter and one in August.
ADDITIONAL EXAM 1, TUESDAY 14/4 from 0900 -> : E-mail me and I will give you a time interval during the day for the exam.
ADDITIONAL EXAM 2: IN AUGUST
Lecture 1: introduction, history, syntax, (in book 1.1 - approx!)
Lecture 2: languages, etc (in book: 1.3)
Lecture 3: Set theory (crash course). Repetition of semantics (in book: 1.5)
Lecture 4: Completeness theorem, Model theory, compactness, applications. (in book: 1.5)
Lecture 5 : continued... Löwenheim-Skolem, soundness. (in book: )
Lecture 6 : continued... proof of completeness thm. (in book: )
Lecture 7 : continued... proof of completeness thm. (in book: )
Lecture 8 : model theory, (elementary) structures, equivalence and embeddings(in book: 1.6)
Lecture 9 : continued...model theory, elementary chains, Tarski-Vaught theorem, Löwenheim-Skolem downwards, open theories, Los-Tarski theorem (in book: 1.6). (And an intermezzo about intuitionistic logic which, in principle, had nothing to do with the course syllabus.)
Lecture 10 : model theory, existential theories, Chang-Los-Suszko theorem, diagrams, (in book: 1.6)
Lecture 11 : model theory, cont... diagrams, Löwenheim-Skolem upwards (revisited) kategorical theories(in book: 1.6)
Lecture 12 : model theory, non-standard analysis (in book: 1.6)
Lecture 13 (Date: 21/10): Cancelled! See also updated schedule. : recursion theory ? (in book: 1.8)
Lecture 14 (Date: 24/10): Cancelled because of automata theory exam! See also updated schedule. recursion theory (in book: 1.8)
Lecture 15 (Date: 28/10): non-standard aritmetic (in book: 1.6)
Lecture 15.5 (Date 31/10): non-standard analysis (in book: 1.6)
Lecture 16: recursion theory : introduction, partial recursive functions (in book: 1.8)
Lecture 17: recursion theory : Gödels \beta-lemma (in book: 1.8)
Lecture 18: recursion theory : Gödel numbers, representability (in book: 1.8 and 1.9)
Lecture 18,5: recursion theory : Gödel numbers, representability (in book: 1.8 and 1.9)
Lecture 19: recursion theory, ibid., incompleteness : (in book: 1.8 and 1.9)
Lecture 20: incompleteness, recursion theory. : (in book: 1.8 and 1.9)
Lecture 20,5: more recursion theory. : (in book: 1.8 and 1.9)
Lecture 21: more recursion theory. : (in book: 1.8 and 1.9)
Lecture 22: even more recursion theory. Rice's (and -Shapiro's) theorem: (in book: 1.8 and 1.9)
Lecture 23: even more recursion theory. A little about relative computability or the arithmetic hierarchy. (in book: 1.8 and 1.9)
Lecture 24: Idem. and oral presentations : (in book: 1.8 and 1.9)
Last Lecture (#25, Date: 5/12). Oral exam, mandatory. No book or notes allowed.
Me, on a beautiful day in a beautiful alley, in a picture by Johan Steensland, taken in 2008.
Göran Hamrin. Address: Lindsbergsgatan 9A, SE-75240 Uppsala, Sweden. Email: Try a combination of my last name, "@" and "math.uu.se".
