26 found
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  1.  46
    Logical Operations and Invariance.Enrique Casanovas - 2007 - Journal of Philosophical Logic 36 (1):33 - 60.
    I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.
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  2. Stable Theories with a New Predicate.Enrique Casanovas & Martin Ziegler - 2001 - Journal of Symbolic Logic 66 (3):1127-1140.
  3.  9
    The Number of Types in Simple Theories.Enrique Casanovas - 1999 - Annals of Pure and Applied Logic 98 (1-3):69-86.
    We continue work of Shelah on the cardinality of families of pairwise incompatible types in simple theories obtaining characterizations of simple and supersimple theories. We develop a local analysis of the number of types in simple theories and we find a new example of a simple unstable theory.
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  4.  5
    Logical Operations and Invariance.Enrique Casanovas - 2007 - Journal of Philosophical Logic 36 (1):33-60.
    I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so-called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.
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  5.  2
    An Exposition of the Compactness of L.Enrique Casanovas & Martin Ziegler - forthcoming - Bulletin of Symbolic Logic:1-9.
    We give an exposition of the compactness of L(QcfC), for any set C of regular cardinals.
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  6.  7
    A Supersimple Nonlow Theory.Enrique Casanovas & Byunghan Kim - 1998 - Notre Dame Journal of Formal Logic 39 (4):507-518.
    This paper presents an example of a supersimple nonlow theory and characterizes its independence relation.
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  7.  7
    Stable Theories with a New Predicate.Enrique Casanovas & Martin Ziegler - 2001 - Journal of Symbolic Logic 66 (3):1127-1140.
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  8.  17
    Omitting Types in Incomplete Theories.Enrique Casanovas & Rafel Farré - 1996 - Journal of Symbolic Logic 61 (1):236-245.
    We characterize omissibility of a type, or a family of types, in a countable theory in terms of non-existence of a certain tree of formulas. We extend results of L. Newelski on omitting $ non-isolated types. As a consequence we prove that omissibility of a family of $ types is equivalent to omissibility of each countable subfamily.
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  9. Simple Theories and Hyperimaginaries. Lecture Notes in Logic, Vol. 39.Enrique Casanovas - 2012 - Bulletin of Symbolic Logic 18 (3):405-406.
     
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  10.  9
    Generic Stability and Stability.Hans Adler, Enrique Casanovas & Anand Pillay - 2014 - Journal of Symbolic Logic 79 (1):179-185.
  11.  10
    Local Supersimplicity and Related Concepts.Enrique Casanovas & Frank O. Wagner - 2002 - Journal of Symbolic Logic 67 (2):744-758.
    We study local strengthenings of the simplicity condition. In particular, we define and study a local Lascar rank, as well as short, low, supershort and superlow theories. An example of a low, non supershort theory is given.
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  12.  22
    Weak Forms of Elimination of Imaginaries.Enrique Casanovas & Rafel Farré - 2004 - Mathematical Logic Quarterly 50 (2):126-140.
    We study the degree of elimination of imaginaries needed for the three main applications: to have canonical bases for types over models, to define strong types as types over algebraically closed sets and to have a Galois correspondence between definably closed sets B such that A ⊆ B ⊆ acl and closed subgroups of the Galois group Aut/A). We also characterize when the topology of the Galois group is the quotient topology.
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  13.  27
    Dividing and Chain Conditions.Enrique Casanovas - 2003 - Archive for Mathematical Logic 42 (8):815-819.
    We obtain a chain condition for dividing in an arbitrary theory and a new and shorter proof of a chain condition result of Shelah for simple theories.
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  14.  20
    Some Remarks on Indiscernible Sequences.Enrique Casanovas - 2003 - Mathematical Logic Quarterly 49 (5):475-478.
    We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of coheirs.
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  15.  8
    Universal Theories and Compactly Expandable Models.Enrique Casanovas & Saharon Shelah - 2019 - Journal of Symbolic Logic 84 (3):1215-1223.
    Our aim is to solve a quite old question on the difference between expandability and compact expandability. Toward this, we further investigate the logic of countable cofinality.
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  16. Imaginarios e hiperimaginarios.Enrique Casanovas - 2003 - Teorema: International Journal of Philosophy 22 (1-2):23-41.
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  17.  14
    Stable Forking and Imaginaries.Enrique Casanovas & Joris Potier - 2018 - Notre Dame Journal of Formal Logic 59 (4):497-502.
    We prove that a theory T has stable forking if and only if Teq has stable forking.
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  18.  15
    Compactly Expandable Models and Stability.Enrique Casanovas - 1995 - Journal of Symbolic Logic 60 (2):673-683.
  19.  14
    Orbits of Subsets of the Monster Model and Geometric Theories.Enrique Casanovas & Luis Jaime Corredor - 2017 - Annals of Pure and Applied Logic 168 (12):2152-2163.
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  20.  2
    Model Theory of Steiner Triple Systems.Silvia Barbina & Enrique Casanovas - 2019 - Journal of Mathematical Logic 20 (2):2050010.
    A Steiner triple system (STS) is a set S together with a collection B of subsets of S of size 3 such that any two elements of S belong to exactly one element of B. It is well known that the class of finite STS has a Fraïssé limit M_F. Here, we show that the theory T of M_F is the model completion of the theory of STSs. We also prove that T is not small and it has quantifier elimination, (...)
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  21.  12
    Preface.Klaus Ambos-Spies, Joan Bagaria, Enrique Casanovas & Ulrich Kohlenbach - 2013 - Annals of Pure and Applied Logic 164 (12):1177.
  22.  10
    Normal Hyperimaginaries.Enrique Casanovas & Joris Potier - 2014 - Archive for Mathematical Logic 53 (5-6):583-591.
    We introduce the notion of normal hyperimaginary and we develop its basic theory. We present a new proof of the Lascar-Pillay theorem on bounded hyperimaginaries based on properties of normal hyperimaginaries. However, the use of the Peter–Weyl theorem on the structure of compact Hausdorff groups is not completely eliminated from the proof. In the second part, we show that all closed sets in Kim-Pillay spaces are equivalent to hyperimaginaries and we use this to introduce an approximation of φ-types for bounded (...)
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  23.  12
    | T|+‐Resplendent Models and the Lascar Group.Enrique Casanovas & Rodrigo Peláez - 2005 - Mathematical Logic Quarterly 51 (6):626-631.
    In this paper we show that in every |T |+-resplendent model N , for every A ⊆ N such that |A | ≤ |T |, the group Autf of strong automorphisms is the least very normal subgroup of the group Aut and the quotient Aut/Autf is the Lascar group over A . Then we generalize this result to every |T |+-saturated and strongly |T |+-homogeneous model.
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  24.  7
    A Test for Expandability.Enrique Casanovas - 1998 - Archive for Mathematical Logic 37 (4):221-234.
    A model $M$ of countable similarity type and cardinality $\kappa$ is expandable if every consistent extension $T_{1}$ of its complete theory with $|T_{1}|\leq \kappa$ is satisfiable in $M$ and it is compactly expandable if every such extension which additionally is finitely satisfiable in $M$ is satisfiable in $M$ . In the countable case and in the case of a model of cardinality $\geq 2^{\omega}$ of a superstable theory without the finite cover property the notions of saturation, expandability and compactness for (...)
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  25. La Lógica En El Siglo XX.Enrique Casanovas - 2005 - In Manuel Garrido (ed.), El Legado Filosófico y Científico Del Siglo Xx. Cátedra. pp. 701--722.
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  26. Mathematical Logic.Enrique Casanovas - 2003 - Archive for Mathematical Logic 42 (8):815.
    .We obtain a chain condition for dividing in an arbitrary theory and a new and shorter proof of a chain condition result of Shelah for simple theories.
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