Graduate Students Seminar-The expressive power of the infinitary logic L_(ω_1 ω)

Title: The expressive power of the infinitary logic L_(ω_1 ω)

 

Abstract: Infinitary logic is a framework that extends first-order logic (FOL) by allowing formulas and sentences of infinite length. In this talk, we will discuss both frameworks and draw differences between the richness of FOL and the expressive power of a specific infinitary logic, L_(ω_1 ω), while determining the limitations that each may have. In addition, we will discuss important applications of this infinitary logic, in particular, Scott's Isomorphism Theorem, which guarantees that every countable structure has a sentence, called the Scott sentence, that describes this structure up to isomorphism. Lastly, we will discuss the computable versions of infinitary formulas and Scott sentences.