After the course the student is familiar with the basic semantical and proof-theoretical aspects of IF logic; the student knows how to interpret and manipulate IF formulas, and is able to follow metamathematical arguments about IF logic.
Prerequisities
Familiarity with first-order logic.
Topics for lectures
1st LESSON
Henkin quantifiers:
-informal presentation of Skolem semantics -a sentence expressing infinity Syntax of IF logic, free and bound variables. Game-theoretical semantics.
2nd LESSON
Hodges' signalling sentence. The correct notion of Skolemization.
Expressive power of sentences:
-the Walkoe-Ehrenfeucht theorem. Panoramic of model-theoretic properties.
3rd LESSON
The debate on compositionality. Team semantics. 1-coherence of first-order logic. The Cameron-Hodges theorem.
Expressive power of open formulas (Kontinen-Vaananen).
4th LESSON
Downward monotonicity, non-contradiction. Substitution Truth equivalence:
-dummy variables in teams (cartesian extension) and in slash sets -locality of sentences
5th LESSON Equivalence in context (1):
-substitution of equivalents
-propositional laws
-shrinking of slash sets
-distribution of quantifiers
6th LESSON
Equivalence in context (2):
-vacuous quantifiers and requantification -quantifier swapping -quantifier extraction -renaming
7th LESSON Equivalence in context (3):
-prenex normal form
-strong regularization
An application: the perfect recall fragment
Active participation in classroom work and written exercises.
Lectures
Mann, Sandu, Sevenster "Independence-Friendly logic: a game-theoretical approach"
Kontinen-Väänänen paper "On definability in Dependence logic"
Course can be a part of advanced studies in mathematics.