\(\lambda\)-satisfiability, \(\lambda\)-consistency property, the downward Löwenheim-Skolem theorem, and the failure of the interpolation theorem for \(L_{\kappa,\kappa}\) with \(\kappa\) a strong limit cardinal of cofinality \(\lambda\)

zbMath0691.03021MaRDI QIDQ582286

Ruggero Ferro

Publication date: 1988

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=RSMUP_1988__80__1_0

zbMATH Keywords

interpolationinfinitary languagesBeth's theoremchain consistency propertieschain modelsdownward Löwenheim-Skolem theorem

Mathematics Subject Classification ID

Interpolation, preservation, definability (03C40) Other infinitary logic (03C75)

Cites Work

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• Seq-consistency property and interpolation theorems
• Consistency property and model existence theorem for second order negative languages with conjunctions and quantifications over sets of cardinality smaller than a strong limit cardinal of denumerable cofinality
• Interpolation theorems for L_k,k²⁺
• Infinitary analogs of theorems from first order model theory