Categoricity results for \(L_{\infty \kappa}\)-free algebras
The paper under review is a compact collection of many interesting and important theorems with many corollaries, examples (the last section tells about concrete algebraic examples) and remarks on \(L_{\infty \kappa}\)-free algebras in a variety of universal algebras. The main results are very shortly described in the summary: ``Let V denote a variety of algebras in a countable language. An algebra is said to be \(L_{\infty \kappa}\)-free if it is Lloys Harrington's method of reindexing first used by Harrington to characterize the 1- section of the superjump. It turns out that the 1-section of R and \({}^ 2E\) is just large enough to contain winning strategies for every \(\Sigma\) \({}^ 0_ 3\)-game. The paper is technical, but accessible to readers familiar with higher type recursion theory.
scientific article; zbMATH DE number 4057490
scientific article