A functorial \(\pi ^ 1_ 2\) singleton
type: Item
instance of: scholarly article
title: A functorial \(\pi ^ 1_ 2\) singleton
zbMATH Open document ID: 0683.03031
DOI: 10.1016/0001-8708(89)90010-8
author: Yanyan Li
published in: Advances in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: If \(\phi\) is a \(\Sigma_ 1\) ZF-formula, M a transitive model of \(V=L\) such that every cardinal satisfies \(\phi\), then there is a cardinal and cofinality preserving class forcing such that in the enlarged model, \(V=L[r]\) holds for some real r, \(0^{\#}\) does not hold, and if \(L_{\alpha}[r]\) is admissible, then \(\phi\) holds for \(\alpha\). The proof uses the technique of Jensen coding.
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E45
zbMATH DE Number: 4118360
zbMATH Keywords: cardinal and cofinality preserving class forcing
zbMATH Keywords: Jensen coding
reviewed by: Péter Komjáth
MaRDI profile type: Publication
full work available at URL: 0001-8708(89)90010-8
OpenAlex ID: W2029290382
cites work: Q3921212
cites work: Some applications of Jensen's coding theorem
cites work: A very absolute Π21 real singleton
cites work: Strong coding
cites work: Analytic determinacy and 0#
cites work: The fine structure of the constructible hierarchy
cites work: Some applications of model theory in set theory
cites work: A Nonconstructible Δ 1 3 Set of Integers
description: scientific article; zbMATH DE number 4118360