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2,164
Homomorphism Preservation Theorems
, 2008
"... The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a firstorder formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existentialpositive formula. Answering a longstanding question in fin ..."
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Cited by 27 (0 self)
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The homomorphism preservation theorem (h.p.t.), a result in classical model theory, states that a firstorder formula is preserved under homomorphisms on all structures (finite and infinite) if and only if it is equivalent to an existentialpositive formula. Answering a longstanding question
On Preservation Theorems for TwoVariable Logic
 MATHEMATICAL LOGIC QUARTERLY
, 1999
"... We show that the existential preservation theorem fails for FO², twovariable firstorder logic. It is known that for all k 3, FO^k does not have an existential preservation theorem, so this settles the last open case, answering a question of Andr'eka, van Benthem, and N'emeti. In contra ..."
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Cited by 9 (1 self)
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We show that the existential preservation theorem fails for FO², twovariable firstorder logic. It is known that for all k 3, FO^k does not have an existential preservation theorem, so this settles the last open case, answering a question of Andr'eka, van Benthem, and N
Preservation Theorems in Finite Model Theory
, 1995
"... We develop various aspects of the finite model theory of Lk (9) andLk 1!(9). We establish the optimality of normal forms for Lk 1!(9) over the class of finite structures and demonstrate separations among descriptive complexity classes within Lk 1!(9). We establish negative results concerning preser ..."
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Cited by 13 (3 self)
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preservation theorems for Lk (9) and Lk 1!(9). We introduce a generalized notion of preservation theorem and establish some positive results concerning "generalized preservation theorems" for firstorder definable classes of nite structures which are closed under extensions.
PRESERVATION THEOREMS IN LUKASIEWICZ MODEL THEORY
"... Abstract. We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BLalgebra. We also prove some a ..."
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appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Morleyization in this framework are discussed and some natural examples of fuzzy theories are presented. 1.
Preservation theorems for countable support forcing iterations
, 2008
"... A major theme of [12] is preservation theorems for iterated forcing. These are theorems of the form “if 〈Pξ:ξ ≤ κ 〉 is a countable support forcing iteration based on 〈 ˙ Qξ:ξ < κ 〉 and each ˙ Qξ has property suchandsuch then Pκ has property thusandso. ” The archetypal preservation theorem is ..."
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A major theme of [12] is preservation theorems for iterated forcing. These are theorems of the form “if 〈Pξ:ξ ≤ κ 〉 is a countable support forcing iteration based on 〈 ˙ Qξ:ξ < κ 〉 and each ˙ Qξ has property suchandsuch then Pκ has property thusandso. ” The archetypal preservation theorem is the
Extension preservation theorems on classes of acyclic finite structures
"... A class of structures satisfies the extension preservation theorem if, on this class, every first order sentence is preserved under extension iff it is equivalent to an existential sentence. We consider different acyclicity notions for hypergraphs (γ, β and αacyclicity and also acyclicity on hyperg ..."
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A class of structures satisfies the extension preservation theorem if, on this class, every first order sentence is preserved under extension iff it is equivalent to an existential sentence. We consider different acyclicity notions for hypergraphs (γ, β and αacyclicity and also acyclicity
Equalityfree Logic: The Method of Diagrams and Preservation Theorems
"... In this article I prove preservation theorems for the positive and for the universalexistential fragment of equalityfree logic. I give a systematic presentation of the method of diagrams for rstorder languages without equality. ..."
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In this article I prove preservation theorems for the positive and for the universalexistential fragment of equalityfree logic. I give a systematic presentation of the method of diagrams for rstorder languages without equality.
Results 1  10
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