Categoricity results for \(L_{\infty \kappa}\)-free algebras
type: Item
instance of: scholarly article
title: Categoricity results for \(L_{\infty \kappa}\)-free algebras
zbMATH Open document ID: 0648.03021
DOI: 10.1016/0168-0072(88)90049-8
author: Paul C. Eklof
author: Alan H. Mekler
published in: Annals of Pure and Applied Logic
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 03C35
Mathematics Subject Classification ID: 08B20
Mathematics Subject Classification ID: 03C75
zbMATH DE Number: 4057490
zbMATH Keywords: definability
zbMATH Keywords: \(L_{\infty \kappa }\)-free algebras
zbMATH Keywords: variety
zbMATH Keywords: reindexing
zbMATH Keywords: \(\Sigma ^ 0_ 3\)-game
zbMATH Keywords: higher type recursion theory
MaRDI profile type: Publication
full work available at URL: 0168-0072(88)90049-8
OpenAlex ID: W2041529775
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description: scientific article; zbMATH DE number 4057490