5 found
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  1.  11
    More on Lower Bounds for Partitioning Α-Large Sets.Henryk Kotlarski, Bożena Piekart & Andreas Weiermann - 2007 - Annals of Pure and Applied Logic 147 (3):113-126.
    Continuing the earlier research from [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001] we show that for the price of multiplying the number of parts by 3 we may construct partitions all of whose homogeneous sets are much smaller than in [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001]. We also show that the Paris–Harrington independent statement remains unprovable if the number of colors is (...)
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  2.  16
    Automorphisms of Countable Recursively Saturated Models of PA: Open Subgroups and Invariant Cuts.Henryk Kotlarski & Bozena Piekart - 1995 - Mathematical Logic Quarterly 41 (1):138-142.
    Let M be a countable recursively saturated model of PA and H an open subgroup of G = Aut. We prove that I = sup {b ∈ M : ∀u < bfu = u and J = inf{b ∈ MH} may be invariant, i. e. fixed by all automorphisms of M.
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  3.  5
    Automorphisms of Models of True Arithmetic: Subgroups Which Extend to a Maximal Subgroup Uniquely.Henryk Kotlarski & Bożena Piekart - 1994 - Mathematical Logic Quarterly 40 (1):95-102.
    We show that if M is a countable recursively saturated model of True Arithmetic, then G = Aut has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut.
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  4.  5
    Automorphisms of Models of True Arithmetic: More on Subgroups Which Extend to a Maximal One Uniquely.Henryk Kotlarski & Bożena Piekart - 2000 - Mathematical Logic Quarterly 46 (1):111-120.
    Continuing the earlier research in [14] we give some more information about nonmaximal open subgroups of G = Aut with unique maximal extension, where ℳ is a countable recursively saturated model of True Arithmetic.
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  5.  7
    On Closed Elementary Cuts in Recursively Saturated Models of Peano Arithmetic.Bożena Piekart - 1993 - Notre Dame Journal of Formal Logic 34 (2):223-230.