A Hanf number for saturation and omission

• Autorzy: John T. Baldwin , Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

Suppose t = (T,T₁,p) is a triple of two countable theories T ⊆ T₁ in vocabularies τ ⊂ τ₁ and a τ₁-type p over the empty set. We show that the Hanf number for the property 'there is a model M₁ of T₁ which omits p, but M₁ ↾ τ is saturated' is essentially equal to the Löwenheim number of second order logic. In Section 4 we make exact computations of these Hanf numbers and note some distinctions between 'first order' and 'second order quantification'. In particular, we show that if κ is uncountable, then $h³(L_{ω,ω}(Q),κ) = h³(L_{ω₁,ω},κ)$, where h³ is the 'normal' notion of Hanf function (Definition 4.12).

Kategorie tematyczne

• 03C85: Second- and higher-order model theory
• 03C52: Properties of classes of models

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 3
• Strony: 255-270

Daty

wydano

2011

Twórcy

autor

John T. Baldwin

• Department of Mathematics, Statistics and Computer Science M/C 249, University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607, U.S.A.

autor

Saharon Shelah

• Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram, Jerusalem 91904, Israel
• Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, U.S.A.

Identyfikatory

DOI

10.4064/fm213-3-5