Logic & Set Theory seminar: Tarskian Satisfaction Predicates, Revisited

21 April 2015, 2.30 PM - 21 April 2015, 3.30 PM

Ali Enayat, University of Gothenburg

Howard House, 4th floor seminar room

This talk reports on joint work with Albert Visser. Suppose we start with a foundational `base theory' B formulated in a language L (such as B = Peano arithmetic, or B = Zermelo-Fraenkel theory), and we extend B to a new theory B+ := B ∪ Σ, where Σ is a set of sentences formulated in the language L+ := L ∪ {S}, such that Σ describes certain prominent features of a Tarskian satisfaction predicate.  I will give an overview of the status of our current knowledge of the relationship between B and B+ in connection with the following four questions (for various canonical choices of B and Σ) :

1. Is B+ semantically conservative over B? In other words, does every model of B expand to a model of B+?
2. Is B+ syntactically conservative over B? In other words, if some L-sentence φ is provabe from B+, then is φ also provable from B?
3. Is B+ interpretable in B?
4. What type of speed-up (if any) does B+ have over B?

Contact information

Organiser: Andrew Brooke-Taylor

Edit this page