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Separating Classes of Groups by FirstOrder Sentences
"... . For various proper inclusions of classes of groups C ae D, we find a group H 2 D and a firstorder sentence ' such that H j= ' but no G 2 C satisfies '. The classes we consider include the classes of finite, finitely presented, finitely generated with and without solvable word ..."
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. For various proper inclusions of classes of groups C ae D, we find a group H 2 D and a firstorder sentence ' such that H j= ' but no G 2 C satisfies '. The classes we consider include the classes of finite, finitely presented, finitely generated with and without solvable word
Ups and Downs of First Order Sentences on Random Graphs
"... Shelah and Spencer [1] proved that the zeroone law holds for the rst order sentences on random graphs G(n; n ) whenever is a fixed positive irrational. This raises the question what zeroone valued functions on the positive irrationals arise as the limit probability of a first order sentence ..."
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Shelah and Spencer [1] proved that the zeroone law holds for the rst order sentences on random graphs G(n; n ) whenever is a fixed positive irrational. This raises the question what zeroone valued functions on the positive irrationals arise as the limit probability of a first order
The expressive power of existential first order sentences of Büchi’s sequential calculus
, 2009
"... The aim of this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or Σnhierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressiv ..."
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The aim of this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or Σnhierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2
The expressive power of existential firstorder sentences of Büchi's sequential calculus
"... The aim of this paper is to study the rstorder theory of the successor, interpreted on nite words. More speci cally, we are interested in the hierarchy based on quanti er alternations (or n hierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive po ..."
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Cited by 5 (0 self)
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is expressible by a rst order sentence (respectively a B 1 sentence).
The Expressive Power of Existential First Order Sentences of Büchi's Sequential Calculus
"... this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or \Sigma nhierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive po ..."
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Cited by 5 (1 self)
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this paper is to study the first order theory of the successor, interpreted on finite words. More specifically, we complete the study of the hierarchy based on quantifier alternations (or \Sigma nhierarchy). It was known (Thomas, 1982) that this hierarchy collapses at level 2, but the expressive
1 FirstOrder Theories
"... A firstorder theory T is a set of firstorder sentences that is closed under the entailment relation, so ϕ ∈ T Not yet just in case T � ϕ. We typically specify a theory by (i) listing its vocabulary and (ii) listing a set of axioms that entails all of the sentences in the theory or at least giving ..."
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A firstorder theory T is a set of firstorder sentences that is closed under the entailment relation, so ϕ ∈ T Not yet just in case T � ϕ. We typically specify a theory by (i) listing its vocabulary and (ii) listing a set of axioms that entails all of the sentences in the theory or at least giving
The Semantics of Predicate Logic as a Programming Language
 JOURNAL OF THE ACM
, 1976
"... Sentences in firstorder predicate logic can be usefully interpreted as programs In this paper the operational and fixpoint semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated It is concluded that operational seman ..."
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Cited by 808 (18 self)
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Sentences in firstorder predicate logic can be usefully interpreted as programs In this paper the operational and fixpoint semantics of predicate logic programs are defined, and the connections with the proof theory and model theory of logic are investigated It is concluded that operational
On the Decision Problem for TwoVariable FirstOrder Logic
, 1997
"... We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity ..."
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Cited by 83 (1 self)
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We identify the computational complexity of the satisfiability problem for FO², the fragment of firstorder logic consisting of all relational firstorder sentences with at most two distinct variables. Although this fragment was shown to be decidable a long time ago, the computational complexity
Results 1  10
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1,339