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

• Autorzy: Saharon Shelah , Pauli Vaisanen
• Języki publikacji: EN

Abstrakty

EN

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 $L_{∞,κ}$-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 of Σ¹₁-equivalence relations are in a prearranged set. Together these results settle the problem of the possible values of No(M) for models of weakly compact cardinality.

Kategorie tematyczne

• 03C75: Other infinitary logic
• 03C55: Set-theoretic model theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 174
• Numer: 2
• Strony: 97-126

Daty

wydano

2002

Twórcy

autor

Saharon Shelah

• Institute of Mathematics, The Hebrew University, Jerusalem, Israel
• Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, U.S.A.

autor

Pauli Vaisanen

• Department of Mathematics, P.O. Box 4, 00014 University of Helsinki, Finland

Identyfikatory

DOI

10.4064/fm174-2-1