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  1. Definability and automorphisms in abstract logics.Xavier Caicedo - 2004 - Archive for Mathematical Logic 43 (8):937-945.
    In any model theoretic logic, Beth’s definability property together with Feferman-Vaught’s uniform reduction property for pairs imply recursive compactness, and the existence of models with infinitely many automorphisms for sentences having infinite models. The stronger Craig’s interpolation property plus the uniform reduction property for pairs yield a recursive version of Ehrenfeucht-Mostowski’s theorem. Adding compactness, we obtain the full version of this theorem. Various combinations of definability and uniform reduction relative to other logics yield corresponding results on the existence of non-rigid (...)
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  • On models with power-like ordering.Saharon Shelah - 1972 - Journal of Symbolic Logic 37 (2):247-267.
    We prove here theorems of the form: if T has a model M in which P 1 (M) is κ 1 -like ordered, P 2 (M) is κ 2 -like ordered ..., and Q 1 (M) if of power λ 1 , ..., then T has a model N in which P 1 (M) is κ 1 '-like ordered ..., Q 1 (N) is of power λ 1 ,.... (In this article κ is a strong-limit singular cardinal, and κ' is (...)
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  • EM constructions for a class of generalized quantifiers.Martin Otto - 1992 - Archive for Mathematical Logic 31 (5):355-371.
    We consider a class of Lindström extensions of first-order logic which are susceptible to a natural Skolemization procedure. In these logics Ehrenfeucht Mostowski (EM) functors for theories with arbitrarily large models can be obtained under suitable restrictions. Characteristic dependencies between algebraic properties of the quantifiers and the maximal domains of EM functors are investigated.Results are applied to Magidor Malitz logic,L(Q <ω), showing e.g. its Hanf number to be equal to ℶω(ℵ1) in the countably compact case. Using results of Baumgartner, the (...)
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  • Automorphism properties of stationary logic.Martin Otto - 1992 - Journal of Symbolic Logic 57 (1):231-237.
    By means of an Ehrenfeucht-Mostowski construction we obtain an automorphism theorem for a syntactically characterized class of Laa-theories comprising in particular the finitely determinate ones. Examples of Laa-theories with only rigid models show this result to be optimal with respect to a classification in terms of prenex quantifier type: Rigidity is seen to hinge on quantification of type $\ldots\forall\ldots\mathbf{\operatorname{stat}}\ldots$ permitting of the parametrization of families of disjoint stationary systems by the elements of the universe.
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  • On the homogeneity property for certain quantifier logics.Heike Mildenberger - 1992 - Archive for Mathematical Logic 31 (6):445-455.
    The local homogeneity property is defined as in [Mak]. We show thatL ωω(Q1) and some related logics do not have the local homogeneity property, whereas cofinality logicL ωω(Q cfω) has the homogeneity property. Both proofs use forcing and absoluteness arguments.
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