# Second order logic - a philosophical and mathematical appraisal, spring 2011

### Lecturer

### Scope

5 cu.

### Type

Advanced studies

### Prerequisites

The course assumes knowledge of Gödel's Completeness and Incompleteness Theorems for predicate (i.e. first order) logic. Also knowledge of basic naive and axiomatic set theory is needed.

### Lectures

Weeks 3-9 and 11-18 Tuesday 14-16 in room C124. No lecture on 22. March.

Easter holiday 21.-27.4.

### Content outline

### Lecture notes In SO7, page 8, proof of the theorem: In the definition of R the implication arrow has to be reversed. Then the proof works.

### Exercises

### Exams

The final exam will be 10.5. at 12-16. If this time is not suitable for someone, let me know.

### Bibliography

There is no course book at the moment. There are chapters on second order logic in at least the following sources:

- Alonzo Church, Introduction to mathematical logic. Vol. I. Princeton University Press, Princeton, N. J., 1956.
- Johan van Benthem, Kees Doets, Higher-order logic. Handbook of philosophical logic, Vol. 1, 189--243, Kluwer Acad. Publ., Dordrecht, 2001.
- Jouko Väänänen, Second-order logic and foundations of mathematics http://mathstat.helsinki.fi/logic/people/jouko.vaananen/secondorder.pdf. Bull. Symbolic Logic 7 (2001), no. 4, 504--520.
- Jouko Väänänen Second order logic, set theory and foundations of mathematics http://mathstat.helsinki.fi/logic/people/jouko.vaananen/second_order_or_set_theory.pdf
- Jouko Väänänen Second order logic or set theory? http://mathstat.helsinki.fi/logic/people/jouko.vaananen/solost.pdf
- An online survey of second and higher order logic: http://plato.stanford.edu/entries/logic-higher-order/
- Maria Manzano: Extensions of first order logic, Cambridge University Press http://www.cambridge.org/fi/knowledge/isbn/item1115231/?site_locale=fi_FI
- Steward Shapiro, Foundations without Foundationalism, (Clarendon press, Oxford 1991/2000).
- Daniel Leivant, Higher order logic, in: Handbook of Logic in Artificial Intelligence and Logic Programming: Deduction methodologies Dov M. Gabbay, Christopher John Hogger, John Alan Robinson (eds.) Oxford University Press, 1994.

### Registration

Did you forget to register? What to do.

### Exercise groups (Start 25.1.2011)

Group | Day | Time | Place | Instructor |
---|---|---|---|---|

1. | Tue | 16-18 | C124 | Jouko Väänänen |