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  1. Hirokazu Nishimura (1994). Boolean Valued and Stone Algebra Valued Measure Theories. Mathematical Logic Quarterly 40 (1):69-75.
    In conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ-field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ-field as well, then all the glorious legacy of classical measure theory is preserved completely.
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  2. Hirokazu Nishimura (1993). A Boolean Transfer Principle From L*‐Algebras to AL*‐Algebras. Mathematical Logic Quarterly 39 (1):241-250.
    Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is (...)
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  3. Hirokazu Nishimura (1993). On a Duality Between Boolean Valued Analysis and Topological Reduction Theory. Mathematical Logic Quarterly 39 (1):23-32.
    By creating an unbounded topological reduction theory for complex Hilbert spaces over Stonean spaces, we can give a category-theoretic duality between Boolean valued analysis and topological reduction theory for complex Hilbert spaces. MSC: 03C90, 03E40, 06E15, 46M99.
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  4. Hirokazu Nishimura (1991). Boolean Valued Dedekind Domains. Mathematical Logic Quarterly 37 (5‐6):65-76.
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  5. Hirokazu Nishimura (1991). Boolean Valued Lie Algebras. Journal of Symbolic Logic 56 (2):731-741.
    In this paper we study a certain class of Lie algebras over commutative von Neumann algebras satisfying a certain finiteness condition. By using Boolean valued methods developed by Takeuti [8]-[11], we will establish the basic structure and representation theorems.
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  6. Hirokazu Nishimura (1991). Foundations of Boolean Valued Algebraic Geometry. Mathematical Logic Quarterly 37 (26‐30):421-438.
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  7. Hirokazu Nishimura (1991). Some Boolean Valued Commutative Algebra. Mathematical Logic Quarterly 37 (23‐24):367-384.
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  8. Hirokazu Nishimura (1990). On the Absoluteness of Types in Boolean Valued Lattices. Mathematical Logic Quarterly 36 (3):241-246.
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  9. Hirokazu Nishimura (1990). Some Connections Between Boolean Valued Analysis and Topological Reduction Theory for C*‐Algebras. Mathematical Logic Quarterly 36 (5):471-479.
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  10. Hirokazu Nishimura (1983). Hauptsatz for Higher-Order Modal Logic. Journal of Symbolic Logic 48 (3):744-751.
  11. Hirokazu Nishimura (1981). Model Theory for Tense Logic: Saturated and Special Models with Applications to the Tense Hierarchy. Studia Logica 40 (2):89 - 98.
    The aims of this paper are: (1) to present tense-logical versions of such classical notions as saturated and special models; (2) to establish several fundamental existence theorems about these notions; (3) to apply these powerful techniques to tense complexity.In this paper we are concerned exclusively with quantifiedK 1 (for linear time) with constant domain. Our present research owes much to Bowen [2], Fine [5] and Gabbay [6].
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  12. Hirokazu Nishimura (1981). The Semantical Characterization of de Dicto in Continuous Modal Model Theory. Mathematical Logic Quarterly 27 (15):233-240.
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  13. Hirokazu Nishimura (1980). A Preservation Theorem for Tense Logic. Mathematical Logic Quarterly 26 (19‐21):331-335.
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  14. Hirokazu Nishimura (1980). Saturated and Special Models in Modal Model Theory With Applications to the Modal and DE RE Hierarchies. Mathematical Logic Quarterly 26 (31):481-490.
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  15. Hirokazu Nishimura (1980). Sequential Method in Quantum Logic. Journal of Symbolic Logic 45 (2):339-352.
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  16. Hirokazu Nishimura (1979). Is the Semantics of Branching Structures Adequate for Chronological Modal Logics? Journal of Philosophical Logic 8 (1):469 - 475.
  17. Hirokazu Nishimura (1979). Is the Semantics of Branching Structures Adequate for Non-Metric Ockhamist Tense Logics? Journal of Philosophical Logic 8 (1):477 - 478.
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  18. Hirokazu Nishimura (1979). On the Completeness of Chronological Logics with Modal Operators. Mathematical Logic Quarterly 25 (31):487-496.
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