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Helmut Seidl, Damian Niwiński (2010)
RAIRO - Theoretical Informatics and Applications
For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e' of alternation-depth 2 and size . Expression e' is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of the resulting expression.
Margarita Otero (2009)
Fundamenta Mathematicae
Let ℳ be an o-minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. We show that a definably compact definably connected group is divisible.
F. Blanchet-Sadri (1990)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Morozov, A.S. (2009)
Sibirskij Matematicheskij Zhurnal
J. Hartmanis (1976)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Henryk Kotlarski (1983)
Fundamenta Mathematicae
Henryk Kotlarski (1984)
Fundamenta Mathematicae
Fred Clare (1976)
Colloquium Mathematicae
Juliette Kennedy, Saharon Shelah (2003)
Fundamenta Mathematicae
In the early 1970’s S. Tennenbaum proved that all countable models of PA₁¯ + ∀₁ -Th(ℕ) are embeddable into the reduced product , where ℱ is the cofinite filter. In this paper we show that if M is a model of PA¯ + ∀₁ - Th(ℕ), and |M| = ℵ₁, then M is embeddable into , where D is any regular filter on ω.
Donald Monk (1970)
Mathematica Scandinavica
Saharon Shelah, Pauli Vaisanen (2002)
Fundamenta Mathematicae
Let κ be an uncountable regular cardinal. Call an equivalence relation on functions from κ into 2 second order definable over H(κ) if there exists a second order sentence ϕ and a parameter P ⊆ H(κ) such that functions f and g from κ into 2 are equivalent iff the structure ⟨ H(κ), ∈, P, f, g ⟩ satisfies ϕ. The possible numbers of equivalence classes of second order definable equivalence relations include all the nonzero cardinals at most κ⁺. Additionally, the possibilities are closed under unions...
Enric Trillas (1992)
Stochastica
Miodrag Rašković (1979)
Publications de l'Institut Mathématique
M. Raskovic (1979)
Publications de l'Institut Mathématique [Elektronische Ressource]
Bernd Borchert, Dietrich Kuske, Frank Stephan (1999)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
Bernd Borchert, Dietrich Kuske, Frank Stephan (2010)
RAIRO - Theoretical Informatics and Applications
Under the assumption that the Polynomial-Time Hierarchy does not collapse we show for a regular language L: the unbalanced polynomial-time leaf language class determined by L equals iff L is existentially but not quantifierfree definable in FO[<, min, max, +1, −1]. Furthermore, no such class lies properly between NP and co-1-NP or NP⊕co-NP. The proofs rely on a result of Pin and Weil characterizing the automata of existentially first-order definable languages.
Matt Kaufmann (1984)
Fundamenta Mathematicae
Sudoplatov, S.V. (2009)
Sibirskij Matematicheskij Zhurnal
Roman Wencel (2009)
Fundamenta Mathematicae
We prove that if ℳ = (M,≤,+,...) is a weakly o-minimal non-valuational structure expanding an ordered group (M,≤,+), then its expansion by a family of "non-valuational" unary predicates remains non-valuational. The paper is based on the author's earlier work on strong cell decomposition for weakly o-minimal non-valuational expansions of ordered groups.
J. Bilý, L. Bukovský (1974)
Fundamenta Mathematicae