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For a cardinal κ and a model M of cardinality κ let No(M) denote the number of nonisomorphic models of cardinality κ which are $L_{\infty, κ}$ -equivalent to M. We prove that for κ a weakly compact cardinal, the question of the possible values of No(M) for models M of cardinality κ is equivalent to the question of the possible numbers of equivalence classes of equivalence relations which are Σ¹₁-definable over $V_{κ}$ . By [SV] it is possible to have a generic extension where the possible numbers of equivalence classes...

The role of the omitting types theorem in infinitary logic.

Jon Barwise (1981)

Archiv für mathematische Logik und Grundlagenforschung

The structure of $ω_{1}$ -like orderings

Victor Harnik, Mark Nadel, Jonathan Stavi (1986)

Fundamenta Mathematicae

The theory of dual groups

A. Mekler, G. Schlitt (1994)

Fundamenta Mathematicae

We study the $L_{\infty, w}$ -theory of sequences of dual groups and give a complete classification of the $L_{\infty, w}$ -elementary classes by finding simple invariants for them. We show that nonstandard models exist.

What the finitization problem is not

A. Simon (1993)

Banach Center Publications

Δ-extension and Hanf-numbers

Juoko Väänänen (1983)

Fundamenta Mathematicae

$λ$ -satisfiability, $λ$ -consistency property, the downward Lowenheim Skolem theorem, and the failure of the interpolation theorem for $L_{k, k}$ with $k$ a strong limit cardinal of cofinality $λ$

Ruggero Ferro (1988)

Rendiconti del Seminario Matematico della Università di Padova

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Scott sentences and a problem of Vaught for mono-uary algebras

Seq-consistency property and interpolation theorems

Strong Maehara and Takeuti type interpolation theorems for $L_{k, k}^{2 +}$

Strong Maehara and Takeuti type interpolation theorems for $L_{k, k}^{2 +}$

Svenonius sentences and Lindström's theory on preservation theorems

The number of $L_{\infty κ}$ -equivalent nonisomorphic models for κ weakly compact

The role of the omitting types theorem in infinitary logic.

The structure of $ω_{1}$ -like orderings

The theory of dual groups

What the finitization problem is not

Δ-extension and Hanf-numbers

$λ$ -satisfiability, $λ$ -consistency property, the downward Lowenheim Skolem theorem, and the failure of the interpolation theorem for $L_{k, k}$ with $k$ a strong limit cardinal of cofinality $λ$

$ω$ -satisfiability, $ω$ -consistency property, and the downward Lowenheim Skolem theorem for $L_{k, k}$

Кодирование псевдобулевых моделей для инфинитарной неклассической логики трансфинитного порядка.

Конструктивные и неконструктивные бесконечные формулы в вычислимых моделях

Мощность моделей теорий исчисления с квантором Хартига.

О числе моделей в $L_{\infty, ω_{1}}$ -теориях. II

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