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PROBABILITIES ON FIRST ORDER MODELS
Miklos Ferenczi
Department of Algebra, Institute of Mathematics, Budapest University of Technology and Economics, Budapest, Hungary
Abstract: It is known that set algebras corresponding to first order models (i.e., cylindric set algebras associated with first order interpretations) are \emph{not} $\sigma$closed, but closed w.r.t. certain infima and suprema i.e.,
\left\exists x \alpha\right=\bigcup_{i\in\omega}\left\alpha(y_i)\right \quad\text{and}\quad \left\forall x \alpha\right=\bigcap_{i\in\omega}\left\alpha(y_i)\right \leqno{(*)}
for \emph{any} infinite subsequence $y_1,y_2,\ldots y_i,\ldots$ of the individuum variables in the language. We investigate probabilities defined on these set algebras and being continuous w.r.t. the suprema and infima in $(*)$. We can not use the usual technics, because these suprema and infima are not the usual unions and intersections of sets. These probabilities are interesting in computer science among others, because the probabilities of the quantifierfree formulas determine that of \emph{any} formula, and the probabilities of the former ones can be measured by statistical methods.
Keywords: probability logic; algebraic logic
Classification (MSC2000): 03B48; 03G15
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Electronic fulltext finalized on: 2 Mar 2006.
This page was last modified: 27 Oct 2006.
© 2006 Mathematical Institute of the Serbian Academy of Science and Arts
© 2006 ELibM and FIZ Karlsruhe / Zentralblatt MATH for
the EMIS Electronic Edition
