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.