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

Lecturer

Jouko Väänänen

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:

1. Alonzo Church, Introduction to mathematical logic. Vol. I. Princeton University Press, Princeton, N. J., 1956.
2. Johan van Benthem, Kees Doets, Higher-order logic. Handbook of philosophical logic, Vol. 1, 189--243, Kluwer Acad. Publ., Dordrecht, 2001.
3. 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.
4. 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
5. Jouko Väänänen Second order logic or set theory? http://mathstat.helsinki.fi/logic/people/jouko.vaananen/solost.pdf
6. An online survey of second and higher order logic: http://plato.stanford.edu/entries/logic-higher-order/
7. Maria Manzano: Extensions of first order logic, Cambridge University Press http://www.cambridge.org/fi/knowledge/isbn/item1115231/?site_locale=fi_FI
8. Steward Shapiro, Foundations without Foundationalism, (Clarendon press, Oxford 1991/2000).
9. 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

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Exercise groups (Start 25.1.2011)