15 found
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  1.  11
    On the Order Between Quantifiers.Juha Oikkonen & Dag Westerstahl - 1989 - Journal of Symbolic Logic 54 (2):631.
  2.  20
    Undefinability of Κ-Well-Orderings in L∞Κ.Juha Oikkonen - 1997 - Journal of Symbolic Logic 62 (3):999 - 1020.
    We prove that the class of trees with no branches of cardinality ≥κ is not RPC definable in L ∞κ when κ is regular. Earlier such a result was known for L κ + κ under the assumption $\kappa^{ . Our main result is actually proved in a stronger form which covers also L ∞λ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality κ.
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  3.  49
    A Recursion Principle for Linear Orderings.Juha Oikkonen - 1992 - Journal of Symbolic Logic 57 (1):82-96.
    The idea of this paper is to approach linear orderings as generalized ordinals and to study how they are made from their initial segments. First we look at how the equality of two linear orderings can be expressed in terms of equality of their initial segments. Then we shall use similar methods to define functions by recursion with respect to the initial segment relation. Our method is based on the use of a game where smaller and smaller initial segments of (...)
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  4.  32
    Jouko Väänänen, A Hierarchy Theorem for Lindstrom Quantifiers, Logic and Abstraction, Essays Dedicated to Per Lindström on His Fiftieth Birthday, Edited by Mats Furberg, Thomas Wetterström, and Claes Åberg, Acta Philosophica Gothoburgensia, No. 1, Acta Universitatis Gothobargensis, Göteborg1986, Pp. 317–323. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):631-631.
  5.  29
    Jan Berg, A Logic of Terms with an Existence Operator, Logic and Abstraction, Essays Dedicated to Per Lindström on His Fiftieth Birthday, Edited by Mats Furberg, Thomas Wetterström, and Claes Åberg, Acta Philosophica Gothoburgensia, No. 1, Acta Universitatis Gothobargensis, Göteborg1986, Pp. 71–94. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):630-631.
  6.  13
    Game-Theoretic Inductive Definability.Juha Oikkonen & Jouko Väänänen - 1993 - Annals of Pure and Applied Logic 65 (3):265-306.
    Oikkonen, J. and J. Väänänen, Game-theoretic inductive definability, Annals of Pure and Applied Logic 65 265-306. We use game-theoretic ideas to define a generalization of the notion of inductive definability. This approach allows induction along non-well-founded trees. Our definition depends on an underlying partial ordering of the objects. In this ordering every countable ascending sequence is assumed to have a unique supremum which enables us to go over limits. We establish basic properties of this induction and examine examples where it (...)
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  7.  9
    Undefinability of $Kappa$-Well-Orderings in $L_{Inftykappa}$.Juha Oikkonen - 1997 - Journal of Symbolic Logic 62 (3):999-1020.
    We prove that the class of trees with no branches of cardinality $\geq\kappa$ is not RPC definable in $L_{\infty\kappa}$ when $\kappa$ is regular. Earlier such a result was known for $L_{\kappa^+\kappa}$ under the assumption $\kappa^{<\kappa} = \kappa$. Our main result is actually proved in a stronger form which covers also $L_{\infty\lambda}$ (and makes sense there) for every strong limit cardinal $\lambda > \kappa$ of cofinality $\kappa$.
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  8.  8
    Review: Stig Kanger, Unavoidability. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):631-631.
  9.  8
    Review: Herbert Hochberg, Some Paradoxes of Prediction, Identity and Quantification. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):631-631.
  10.  25
    On Ehrenfeucht-Fraïssé Equivalence of Linear Orderings.Juha Oikkonen - 1990 - Journal of Symbolic Logic 55 (1):65-73.
    C. Karp has shown that if α is an ordinal with ω α = α and A is a linear ordering with a smallest element, then α and $\alpha \bigotimes A$ are equivalent in L ∞ω up to quantifer rank α. This result can be expressed in terms of Ehrenfeucht-Fraïssé games where player ∀ has to make additional moves by choosing elements of a descending sequence in α. Our aim in this paper is to prove a similar result for Ehrenfeucht-Fraïssé (...)
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  11.  4
    A Hierarchy Theorem for Lindstrom Quantifiers.Juha Oikkonen & Jouko Vaananen - 1989 - Journal of Symbolic Logic 54 (2):631.
  12.  5
    Review: Jan Berg, A Logic of Terms with an Existence Operator. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):630-631.
  13.  4
    Review: Christian Bennet, Mats Furberg, Thomas Wetterstrom, Claes Aberg, On a Problem by D. Guaspari. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):630-630.
  14.  4
    Review: Jouko Vaananen, A Hierarchy Theorem for Lindstrom Quantifiers. [REVIEW]Juha Oikkonen - 1989 - Journal of Symbolic Logic 54 (2):631-631.
  15.  31
    Logical operations and iterated deep languages.Juha Oikkonen - 1983 - Studia Logica 42:243.
    We discuss an abstract notion of a logical operation and corresponding logics. It is shown that if all the logical operations considered are implicitely definable in a logic *, then the same holds also for the logic obtained from these operations. As an application we show that certain iterated forms of infinitely deep languages are implicitely definable in game quantifier languages. We consider also relations between structures and show that Karttunen's characterization of elementary equivalence for the ordinary infinitely deep languages (...)
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