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

zbMath0365.02006MaRDI QIDQ1241504

Ruggero Ferro

Publication date: 1977

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_1976__55__123_0

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other infinitary logic (03C75) Other classical first-order model theory (03C68)

Related Items

Karp's interpolation theorem for some classes of infinitary languages, An analysis of Karp's interpolation theorem and the notion of k- consistency property, Strong Maehara and Takeuti type interpolation theorems for \(L_{k,k}^{2+}\), Strong Maehara and Takeuti type interpolation theorems for \(L^{2+}_{k,k}\), \(\lambda\)-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 \(\lambda\), \(\omega\)-satisfiability, \(\omega\)-consistency property, and the downward Löwenheim Skolem theorem for \(L_{\kappa,\kappa}\), Seq-consistency property and interpolation theorems

Cites Work

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• Model theory for infinitary logic. Logic with countable conjunctions and finite quantifiers
• Two interpolation theorems for a predicate calculus
• On the model theory of denumerably long formulas with finite strings of quantifiers