University Seminars:Logic Across Disciplines-Structural Properties of Spectra and Omega-Spectra

Title: Structural Properties of Spectra and Omega-Spectra
Speaker:Alexandra Soskova, Sofia University, Bulgaria
Date and Time: Thursday, March 22, 2018, 12:30-1:30 PM
Place: Rome Hall (801 22nd Street), Room 531

Abstract: We consider the degree spectrum of a structure from the point of view of enumeration reducibility and omega-enumeration reducibility. We will give an overview of several structural properties of degree spectra and their co-spectra, such as a minimal pair theorem and the existence of quasi-minimal degrees for degree spectra and receive as a corollary some fundamental theorems in enumeration degrees. We will show that every countable ideal of enumeration degrees is a co-spectrum of a structure and if a degree spectrum has a countable base then it has a least enumeration degree. Next we investigate the omega-enumeration co-spectra and show that not every countable ideal of omega-enumeration degrees is an omega-co-spectrum of a structure.