Polish G-spaces, the generalized model theory and complexity

Abstract

Given Polish space $\mathbf{Y}$ and continuous language $L$ we study the corresponding logic $\mathsf{Iso}(\mathbf{Y})$-space ${\mathbf{Y}}_L$. We build a framework of generalized model theory towards analysis of Borel/algorithmic complexity of subsets of ${\mathbf{Y}}_L^k\times (\mathsf{Iso}(\mathbf{Y}{)}^l$. The paper substantially develops (and corrects) Section 5 of arxiv:1304.5135. The second version is extended by Remark 3.4.

33 pages

References in corpus (3)

• Model theoretic forcing in analysis
• Bounds on Continuous Scott Rank
• Representing Polish groupoids via metric structures