46 found
Order:
  1.  13
    On the Decidability of the Theory of Modules Over the Ring of Algebraic Integers.Sonia L'Innocente, Carlo Toffalori & Gena Puninski - 2017 - Annals of Pure and Applied Logic 168 (8):1507-1516.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  2.  7
    The Ziegler Spectrum of the Ring of Entire Complex Valued Functions.Sonia L’Innocente, Françoise Point, Gena Puninski & Carlo Toffalori - 2019 - Journal of Symbolic Logic 84 (1):160-177.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  3.  41
    Notes on Local o‐Minimality.Carlo Toffalori & Kathryn Vozoris - 2009 - Mathematical Logic Quarterly 55 (6):617-632.
    We introduce and study some local versions of o-minimality, requiring that every definable set decomposes as the union of finitely many isolated points and intervals in a suitable neighbourhood of every point. Motivating examples are the expansions of the ordered reals by sine, cosine and other periodic functions.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  4.  25
    Decidability of the Theory of Modules Over Commutative Valuation Domains.Gennadi Puninski, Vera Puninskaya & Carlo Toffalori - 2007 - Annals of Pure and Applied Logic 145 (3):258-275.
    We prove that, if V is an effectively given commutative valuation domain such that its value group is dense and archimedean, then the theory of all V-modules is decidable.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  5.  7
    Decidability of the Theory of Modules Over Prüfer Domains with Infinite Residue Fields.Lorna Gregory, Sonia L’Innocente, Gena Puninski & Carlo Toffalori - 2018 - Journal of Symbolic Logic 83 (4):1391-1412.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  6.  8
    Lattice Ordered O -Minimal Structures.Carlo Toffalori - 1998 - Notre Dame Journal of Formal Logic 39 (4):447-463.
    We propose a notion of -minimality for partially ordered structures. Then we study -minimal partially ordered structures such that is a Boolean algebra. We prove that they admit prime models over arbitrary subsets and we characterize -categoricity in their setting. Finally, we classify -minimal Boolean algebras as well as -minimal measure spaces.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  7.  19
    The Theory of {Vec Z}C(2)^2-Lattices is Decidable.Stefano Baratella & Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):91-104.
    For arbitrary finite group $G$ and countable Dedekind domain $R$ such that the residue field $R/P$ is finite for every maximal $R$ -ideal $P$ , we show that the localizations at every maximal ideal of two $RG$ -lattices are isomorphic if and only if the two lattices satisfy the same first order sentences. Then we investigate generalizations of the above results to arbitrary $R$ -torsion-free $RG$ -modules and we apply the previous results to show the decidability of the theory of (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  8.  16
    The Decision Problem for {Vec Z}C(P^3)-Lattices with P Prime.Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2):127-142.
    We show undecidability for lattices over a group ring ${\vec Z} \, G$ where $G$ has a cyclic subgroup of order $p^3$ for some odd prime $p$ . Then we discuss the decision problem for ${\vec Z} \, G$ -lattices where $G$ is a cyclic group of order 8, and we point out that a positive answer implies – in some sense – the solution of the “wild $\Leftrightarrow$ undecidable” conjecture.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  9.  12
    An Undecidability Theorem for Lattices Over Group Rings.Carlo Toffalori - 1997 - Annals of Pure and Applied Logic 88 (2-3):241-262.
    Let G be a finite group, T denote the theory of Z[G]-lattices . It is shown that T is undecidable when there are a prime p and a p-subgroup S of G such that S is cyclic of order p4, or p is odd and S is non-cyclic of order p2, or p = 2 and S is a non-cyclic abelian group of order 8 . More precisely, first we prove that T is undecidable because it interprets the word problem (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  10.  7
    On the Undecidability of Some Classes of Abelian-by-Finite Groups.Annalisa Marcja, Mike Prest & Carlo Toffalori - 1993 - Annals of Pure and Applied Logic 62 (2):167-173.
    Let G be a finite group. For every formula ø in the language of groups, let K denote the class of groups H such that ø is a normal abelian subgroup of H and the quotient group H;ø is isomorphic to G. We show that if G is nilpotent and its order is not square-free, then there exists a formula ø such that the theory of K is undecidable.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  11.  21
    Wildness Implies Undecidability for Lattices Over Group Rings.Carlo Toffalori - 1997 - Journal of Symbolic Logic 62 (4):1429-1447.
  12.  17
    Decidability for ℤ[G]‐Modules When G is Cyclic of Prime Order.Carlo Toffalori - 1996 - Mathematical Logic Quarterly 42 (1):369-378.
    We consider the decision problem for modules over a group ring ℤ[G], where G is a cyclic group of prime order. We show that it reduces to the same problem for a class of certain abelian structures, and we obtain some partial decidability results for this class.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  13.  16
    Classification Theory for Abelian Groups with an Endomorphism.Annalisa Marcja, Mike Prest & Carlo Toffalori - 1991 - Archive for Mathematical Logic 31 (2):95-104.
  14.  10
    Abelian‐by‐G Groups, for G Finite, From the Model Theoretic Point of View.Annalisa Marcja & Carlo Toffalori - 1994 - Mathematical Logic Quarterly 40 (1):125-131.
    Let G be a finite group. We prove that the theory af abelian-by-G groups is decidable if and only if the theory of modules over the group ring ℤ[G] is decidable. Then we study some model theoretic questions about abelian-by-G groups, in particular we show that their class is elementary when the order of G is squarefree.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  15.  5
    Some Decidability Results for ℤ[G]‐Modules When G is Cyclic of Squarefree Order.Carlo Toffalori - 1996 - Mathematical Logic Quarterly 42 (1):433-445.
    We extend the analysis of the decision problem for modules over a group ring ℤ[G] to the case when G is a cyclic group of squarefree order. We show that separated ℤ[G]-modules have a decidable theory, and we discuss the model theoretic role of these modules within the class of all ℤ[G]-modules. The paper includes a short analysis of the decision problem for the theories of modules over ℤ[ζm], where m is a positive integer and ζm is a primitive mth (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  16.  13
    The Theory of [Mathematical Formula]-Lattices is Decidable.Stefano Baratella & Carlo Toffalori - 1997 - Archive for Mathematical Logic 36 (2).
    Direct download  
     
    Export citation  
     
    Bookmark  
  17.  1
    Classifying Pairs of Equivalence Relations.Carlo Toffalori - 1991 - Notre Dame Journal of Formal Logic 32 (4):637-650.
  18. Stability for Pairs of Equivalence Relations.Carlo Toffalori - 1990 - Notre Dame Journal of Formal Logic 32 (1):112-128.
  19.  15
    The Boolean Spectrum of an $o$-Minimal Theory.Charles Steinhorn & Carlo Toffalori - 1989 - Notre Dame Journal of Formal Logic 30 (2):197-206.
  20.  8
    Comparing First Order Theories of Modules Over Group Rings.Saverio Cittadini & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (1):147-156.
    We consider R-torsionfree modules over group rings RG, where R is a Dedekind domain and G is a finite group. In the first part of the paper [4] we compared the theory T of all R-torsionfree RG-modules and the theory T0 of RG-lattices , and we realized that they are almost always different. Now we compare their behaviour with respect to decidability, when RG-lattices are of finite, or wild representation type.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  21.  11
    On Pairs of Free Modules Over a Dedekind Domain.Saverio Cittadini & Carlo Toffalori - 2006 - Archive for Mathematical Logic 45 (1):75-95.
    The study of pairs of modules (over a Dedekind domain) arises from two different perspectives, as a starting step in the analysis of tuples of submodules of a given module, or also as a particular case in the analysis of Abelian structures made by two modules and a morphism between them. We discuss how these two perspectives converge to pairs of modules, and we follow the latter one to obtain an alternative approach to the classification of pairs of torsionfree objects. (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  22.  4
    Decidability of the Theory of Modules Over Prüfer Domains with Dense Value Groups.Lorna Gregory, Sonia L'Innocente & Carlo Toffalori - 2019 - Annals of Pure and Applied Logic 170 (12):102719.
    We provide algebraic conditions ensuring the decidability of the theory of modules over effectively given Prüfer (in particular Bézout) domains whose localizations at maximal ideals have dense value groups. For Bézout domains, these conditions are also necessary.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  23.  2
    The Torsion‐Free Part of the Ziegler Spectrum of Orders Over Dedekind Domains.Lorna Gregory, Sonia L'Innocente & Carlo Toffalori - 2020 - Mathematical Logic Quarterly 66 (1):20-36.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  24.  23
    Filling Certain Cuts in Discrete Weakly o-Minimal Structures.Stefano Leonesi & Carlo Toffalori - 2005 - Mathematical Logic Quarterly 51 (2):145.
    Discrete weakly o-minimal structures, although not so stimulating as their dense counterparts, do exhibit a certain wealth of examples and pathologies. For instance they lack prime models and monotonicity for definable functions, and are not preserved by elementary equivalence. First we exhibit these features. Then we consider a countable theory of weakly o-minimal structures with infinite definable discrete subsets and we study the Boolean algebra of definable sets of its countable models.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  25.  34
    On the Boolean Algebras of Definable Sets in Weakly o‐Minimal Theories.Stefano Leonesi & Carlo Toffalori - 2004 - Mathematical Logic Quarterly 50 (3):241-248.
    We consider the sets definable in the countable models of a weakly o-minimal theory T of totally ordered structures. We investigate under which conditions their Boolean algebras are isomorphic , in other words when each of these definable sets admits, if infinite, an infinite coinfinite definable subset. We show that this is true if and only if T has no infinite definable discrete subset. We examine the same problem among arbitrary theories of mere linear orders. Finally we prove that, within (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  26.  4
    Weakly Minimal Modules Over Integral Group Rings and Over Related Classes of Rings.Stefano Leonesi, Sonia L'Innocente & Carlo Toffalori - 2005 - Mathematical Logic Quarterly 51 (6):613-625.
    A module is weakly minimal if and only if every pp-definable subgroup is either finite or of finite index. We study weakly minimal modules over several classes of rings, including valuation domains, Prüfer domains and integral group rings.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  27.  2
    Decidability for ℤ2 G-Lattices When G Extends the Noncyclic Group of Order 4.Annalisa Marcja & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (2):203-212.
  28.  8
    Decidability for ℤ2G‐Lattices When G Extends the Noncyclic Group of Order 4.Annalisa Marcja & Carlo Toffalori - 2002 - Mathematical Logic Quarterly 48 (2):203-212.
    Let G be the direct sum of the noncyclic groupof order four and a cyclic groupwhoseorderisthe power pn of some prime p. We show that ℤ2G-lattices have a decidable theory when the cyclotomic polynomia equation image is irreducible modulo 2ℤ for every j ≤ n. More generally we discuss the decision problem for ℤ2G-lattices when G is a finite group whose Sylow 2-subgroups are isomorphic to the noncyclic group of order four.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  29.  7
    On Cantor-Bendixson Spectra Containing (1,1). II.Annalisa Marcja & Carlo Toffalori - 1985 - Journal of Symbolic Logic 50 (3):611-618.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  30.  1
    On Pseudo ‐N0‐Categorical Theories.Annalisa Marcja & Carlo Toffalori - 1984 - Mathematical Logic Quarterly 30 (35):533-540.
  31.  17
    On Pseudo -N0-Categorical Theories.Annalisa Marcja & Carlo Toffalori - 1984 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 30 (35):533-540.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  32.  29
    On the Elementarity of Some Classes of Abelian-by-Infinite Groups.Annalisa Marcja & Carlo Toffalori - 1999 - Studia Logica 62 (2):201-213.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  33.  6
    Towards the Decidability of the Theory of Modules Over Finite Commutative Rings.Gena Puninski & Carlo Toffalori - 2009 - Annals of Pure and Applied Logic 159 (1-2):49-70.
    On the basis of the Klingler–Levy classification of finitely generated modules over commutative noetherian rings we approach the old problem of classifying finite commutative rings R with a decidable theory of modules. We prove that if R is wild, then the theory of all R-modules is undecidable, and verify decidability of this theory for some classes of tame finite commutative rings.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  34.  8
    1918-2018: Cantor and infinity in today’s high school.Carlo Toffalori - 2020 - Science and Philosophy 8 (1):119-129.
    In the first centenary of Cantor's death, we discuss how to introduce his life, his works and his theories about mathematical infinity to today's students. Keywords: proper and improper infinite, cardinal number, countable set, continuum, continuum hypothesis. Sunto Nel primo centenario della scomparsa di Cantor, si discute come presentare la sua vita, le sue opere e le sue teorie sull’infinito agli studenti di oggi. Parole chiave: infinito proprio e improprio, numero cardinale, numerabile, continuo, ipotesi del continuo.
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  35.  5
    Comparing First Order Theories of Modules Over Group Rings II: Decidability: Decidability.Carlo Toffalori & S. Cittadini - 2002 - Mathematical Logic Quarterly 48 (4):483-498.
    We consider R-torsionfree modules over group rings RG, where R is a Dedekind domain and G is a finite group. In the first part of the paper [4] we compared the theory T of all R-torsionfree RG-modules and the theory T0 of RG-lattices , and we realized that they are almost always different. Now we compare their behaviour with respect to decidability, when RG-lattices are of finite, or wild representation type.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  36.  4
    Cantor-Bendixson Spectra of "W"-Stable Theories.Carlo Toffalori - 1987 - Notre Dame Journal of Formal Logic 28:259-275.
  37.  12
    Locally P‐ℵ0‐Categorical Theories.Carlo Toffalori - 1986 - Mathematical Logic Quarterly 32 (19‐24):341-348.
  38.  23
    Locally P-ℵ0-Categorical Theories.Carlo Toffalori - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (19-24):341-348.
  39.  34
    On Complex Exponentiation Restricted to the Integers.Carlo Toffalori & Kathryn Vozoris - 2010 - Journal of Symbolic Logic 75 (3):955-970.
    We provide a first order axiomatization of the expansion of the complex field by the exponential function restricted to the subring of integers modulo the first order theory of (Z, +, ·).
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  40.  13
    P‐ℵ0‐Categorical Lattice‐Ordered Structures.Carlo Toffalori - 1989 - Mathematical Logic Quarterly 35 (1):23-28.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  41.  24
    P-ℵ0-Categorical Lattice-Ordered Structures.Carlo Toffalori - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (1):23-28.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  42.  9
    Simple Pairs of Equivalence Relations.Carlo Toffalori - 1991 - Mathematical Logic Quarterly 37 (26‐30):401-410.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  43.  21
    Simple Pairs of Equivalence Relations.Carlo Toffalori - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (26-30):401-410.
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  44.  4
    The Decision Problem For...-Lattices With..Carlo Toffalori - 1998 - Archive for Mathematical Logic 37 (2).
    Direct download  
     
    Export citation  
     
    Bookmark  
  45.  3
    The Decision Problem for [Mathematical Formula]-Lattices with [Mathematical Formula] Prime.Carlo Toffalori - 1997 - Archive for Mathematical Logic 36 (2).
    Direct download  
     
    Export citation  
     
    Bookmark  
  46.  10
    Weakly o-Minimal Expansions of Boolean Algebras.Carlo Toffalori & S. Leonesi - 2001 - Mathematical Logic Quarterly 47 (2):223-238.
    We propose a definition of weak o-minimality for structures expanding a Boolean algebra. We study this notion, in particular we show that there exist weakly o-minimal non o-minimal examples in this setting.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark