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Predicate Calculus for *Boolean* *Valued* *Functions*. Part VIII Shunichi Kobayashi

, 1999

"... Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of Boolean valued functions with respect to partitions. Such a theory is an analogy of usual predicate logic. MML Identifier: BVFUNC16. WWW: ..."

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Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of

*Boolean**valued**functions*with respect to partitions. Such a theory is an analogy of usual predicate logic. MML Identifier: BVFUNC16. WWW:###
Predicate Calculus for *Boolean* *Valued* *Functions*. Part XII Shunichi Kobayashi

"... Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of Boolean valued functions with respect to partitions. Such a theory is an analogy of ordinary predicate logic. MML Identifier: BVFUNC24. ..."

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Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of

*Boolean**valued**functions*with respect to partitions. Such a theory is an analogy of ordinary predicate logic. MML Identifier: BVFUNC24.###
Predicate Calculus for *Boolean* *Valued* *Functions*. Part XII Shunichi Kobayashi

"... Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of Boolean valued functions with respect to partitions. Such a theory is an analogy of ordinary predicate logic. MML Identifier:BVFUNC24. WWW:http://mizar.org/JFM/Vol11/bvfunc24.html ..."

Abstract
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Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of

*Boolean**valued**functions*with respect to partitions. Such a theory is an analogy of ordinary predicate logic. MML Identifier:BVFUNC24. WWW:http://mizar.org/JFM/Vol11/bvfunc24.html###
Propositional Calculus for *Boolean* *Valued* *Functions*. Part VIII Shunichi Kobayashi Matsumoto University

"... Summary. In this paper, we proved some elementary propositional calculus formulae for Boolean valued functions. ..."

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Summary. In this paper, we proved some elementary propositional calculus formulae for

*Boolean**valued**functions*.###
Six Variable Predicate Calculus for *Boolean* *Valued* *Functions*. Part I Shunichi Kobayashi

"... Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of Boolean valued functions with respect to partitions. Such a theory is an analogy of ordinary predicate logic. MML Identifier: BVFUNC23. ..."

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Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of

*Boolean**valued**functions*with respect to partitions. Such a theory is an analogy of ordinary predicate logic. MML Identifier: BVFUNC23.###
Propositional Calculus for *Boolean* *Valued* *Functions*. Part VII Shunichi Kobayashi Matsumoto University

"... Summary. In this paper, we proved some elementary propositional calculus formulae for Boolean valued functions. MML Identifier:BVFUNC25. WWW:http://mizar.org/JFM/Vol15/bvfunc25.html The articles [4], [3], [2], and [1] provide the notation and terminology for this paper. We use the following conventi ..."

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Summary. In this paper, we proved some elementary propositional calculus formulae for

*Boolean**valued**functions*. MML Identifier:BVFUNC25. WWW:http://mizar.org/JFM/Vol15/bvfunc25.html The articles [4], [3], [2], and [1] provide the notation and terminology for this paper. We use the following###
Propositional Calculus for *Boolean* *Valued* *Functions*. Part VII Shunichi Kobayashi Matsumoto University

"... Summary. In this paper, we proved some elementary propositional calculus formulae ..."

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Summary. In this paper, we proved some elementary propositional calculus formulae

###
*Boolean-valued* Term Models

, 2007

"... We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarsk ..."

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We construct

*Boolean-valued*term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum### REFERENCES

"... Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of Boolean valued functions with respect to partitions. Such a theory is an analogy of usual predicate logic. MML Identifier: BVFUNC17. ..."

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Summary. In this paper, we proved some elementary predicate calculus formulae containing the quantifiers of

*Boolean**valued**functions*with respect to partitions. Such a theory is an analogy of usual predicate logic. MML Identifier: BVFUNC17.###
*Boolean-Valued* Introduction to the Theorv of Vector Lattices

"... The theory of vector lattices appeared in early thirties of this century and is connected with the names of L. V. Kantorovich, F. Riesz, and H. Freudenthal. The study of vector spaces equipped with an order relation compatible with a given norm ..."

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The theory of vector lattices appeared in early thirties of this century and is connected with the names of L. V. Kantorovich, F. Riesz, and H. Freudenthal. The study of vector spaces equipped with an order relation compatible with a given norm