On the Search for a Finitizable Algebraization of First Order Logic
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On the Search for a Finitizable Algebraization of First Order Logic
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| Id. |
46372656 |
| Idioma |
inglés
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| Titulo |
On the Search for a Finitizable Algebraization of First Order Logic |
| Autor(es) |
Ildikó Sain
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| Localización |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.4734
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
We give an algebraic version of first order logic without equality in which the class of representable algebras forms a finitely based equational class. Further, the representables are defined in terms of set algebras, and all operations of the latter are permutation invariant. The algebraic form of this result is Theorem 1 (a concrete version of which is given by Theorems 1.8 and 3.2), while its logical form is Corollary 4.2. For first order logic with equality we give a result weaker than the one for first order logic without equality. Namely, in this case --- instead of finitely axiomatizing the corresponding class of all representable algebras --- we finitely axiomatize only the equational theory of that class. See subsection 5.1, especially Remark 5.5 there. The proof of Theorem 1 is elaborated in sections 2 and 3. These sections contain theorems which are interesting of their own rights, too, e.g. Theorem 3.2 is a purely semigroup theoretic result. Cf. also "Further main result...
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| Tipo |
application/postscript
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| Palabras clave |
algebraic logic
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| Tipo de recurso |
Texto Narrativo
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| Formatos |
application/postscript
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| Requerimientos técnicos |
Browser: Any
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| Relación |
[IsBasedOn] http://www.math-inst.hu/pub/algebraic-logic/fin-abst.ps
[References] 10.1.1.39.7382
[References] 10.1.1.31.5413
[References] 10.1.1.17.6304
[References] 10.1.1.17.6577
[References] 10.1.1.10.8860
[References] 10.1.1.17.6304
[References] 10.1.1.25.8934
[References] 10.1.1.31.3566
[References] 10.1.1.75.6465
[References] 10.1.1.80.8650
[References] 10.1.1.97.7313
[References] 10.1.1.48.6730
[References] 10.1.1.23.4801
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| Fecha de contribución |
24-jul-2009 |
| Contacto |
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