A Theory of Boolean Valued Functions and Partitions

Shunichi Kobayashi

Shinshu University, Nagano

Kui Jia

Shinshu University, Nagano

Summary.

In this paper, we define Boolean valued functions. Some of their algebraic properties are proved. We also introduce and examine the infimum and supremum of Boolean valued functions and their properties. In the last section, relations between Boolean valued functions and partitions are discussed.

MML Identifier: BVFUNC_1

Contents (PDF format)

1. Boolean Operations
2. Boolean Valued Functions
3. Infimum and Supremum
4. Boolean Valued Functions and Partitions

Bibliography

[1] Grzegorz Bancerek. Sequences of ordinal numbers. Journal of Formalized Mathematics, 1, 1989.

[2] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[5] Shunichi Kobayashi and Kui Jia. A theory of partitions. Part I. Journal of Formalized Mathematics, 10, 1998.

[6] Jaroslaw Kotowicz. Monotone real sequences. Subsequences. Journal of Formalized Mathematics, 1, 1989.

[7] Adam Naumowicz and Mariusz Lapinski. On \tone\ reflex of topological space. Journal of Formalized Mathematics, 10, 1998.

[8] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Journal of Formalized Mathematics, 5, 1993.

[9] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.

[10] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.

[11] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[12] Andrzej Trybulec. Function domains and Fr\aenkel operator. Journal of Formalized Mathematics, 2, 1990.

[13] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[14] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[15] Edmund Woronowicz. Interpretation and satisfiability in the first order logic. Journal of Formalized Mathematics, 2, 1990.

[16] Edmund Woronowicz. Many-argument relations. Journal of Formalized Mathematics, 2, 1990.