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  1. Juha Oikkonen (1997). Undefinability of $Kappa$-Well-Orderings in $L_{Inftykappa}$. 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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  2. Juha Oikkonen (1997). Undefinability of Κ-Well-Orderings in L∞Κ. 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. Juha Oikkonen & Jouko Väänänen (1993). Game-Theoretic Inductive Definability. Annals of Pure and Applied Logic 65 (3):265-306.
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  4. Juha Oikkonen (1992). A Recursion Principle for Linear Orderings. 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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  5. Juha Oikkonen (1990). On Ehrenfeucht-Fraïssé Equivalence of Linear Orderings. 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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  6. Juha Oikkonen (1989). Bennet Christian. On a Problem by D. Guaspari, Logic and Abstraction, Essays Dedicated to Per Lindström on His Fiftieth Birthday, Edited by Furberg Mats, Wetterström Thomas, and Åberg Claes, Acta Philosophica Gothoburgensia, No. 1, Acta Universitatis Gothobargensis, Göteborg 1986, Pp. 61–69. [REVIEW] Journal of Symbolic Logic 54 (2):630-630.
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  7. Juha Oikkonen (1989). Review: Christian Bennet, Mats Furberg, Thomas Wetterstrom, Claes Aberg, On a Problem by D. Guaspari. [REVIEW] Journal of Symbolic Logic 54 (2):630-630.
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  8. Juha Oikkonen (1989). Review: Dag Westerstahl, On the Order Between Quantifiers. [REVIEW] Journal of Symbolic Logic 54 (2):631-631.
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  9. Juha Oikkonen (1989). Review: Herbert Hochberg, Some Paradoxes of Prediction, Identity and Quantification. [REVIEW] Journal of Symbolic Logic 54 (2):631-631.
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  10. Juha Oikkonen (1989). Review: Jan Berg, A Logic of Terms with an Existence Operator. [REVIEW] Journal of Symbolic Logic 54 (2):630-631.
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  11. Juha Oikkonen (1989). Review: Jouko Vaananen, A Hierarchy Theorem for Lindstrom Quantifiers. [REVIEW] Journal of Symbolic Logic 54 (2):631-631.
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  12. Juha Oikkonen (1989). Review: Stig Kanger, Unavoidability. [REVIEW] Journal of Symbolic Logic 54 (2):631-631.
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  13. Juha Oikkonen (1989). Ranger Stig, Unavoidability, Logic and Abstraction, Essays Dedicated to Per Lindström on His Fiftieth Birthday, Edited by Furberg Mats, Wetterström Thomas, and Åberg Claes, Acta Philosophica Gothoburgensia, No. 1, Acta Universitatis Gothobargensis, Göteborg 1986, Pp. 227–236. [REVIEW] Journal of Symbolic Logic 54 (2):631-631.
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  14. Juha Oikkonen (1983). Logical Operations and Iterated Infinitely Deep Languages. Studia Logica 42 (2-3):243 - 249.
    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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