# 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

https://store.fmi.uni-sofia.bg/fmi/logic/asoskova/**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.