We will be interested here in algebraic structures defined within the realm of ordered sets. These structures play an eminent role in semantics of various logical calculi. In developing a theory of these structures, two ways are possible, either to begin with the most perfect structure i.e. Boolean algebras and relax gradually its requirements descending to less organized structures or to begin with the least perfect structures and gradually add requirements to ascend to more organized structures. Either approach has its merits, and here we settle with the latter so we begin with the minimal sound structure and subsequently add more features.
KeywordsTopological Space Boolean Algebra Distributive Lattice Algebraic Structure Unit Element
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- [Birkhoff67]G. Birkhoff, Lattice Theory, AMS, Providence, 1940 (3rd ed., 1967 ).Google Scholar
- [Boole847]G. Boole, The Mathematical Analysis of Logic, Cambridge, 1847.Google Scholar
- [Rasiowa74]H. Rasiowa, An Algebraic Approach to Non—Classical Logics, North Holland, 1974.Google Scholar
- [Rasiowa—Sikorski63]H. Rasiowa and R. Sikorski, The Mathematics of Meta-mathematics, PWN-Polish Scientific Publishers, Warszawa, 1963.Google Scholar
- [Schröder895]E. Schröder, Algebra der Logic, Leipzig, 1890–1895.Google Scholar
- [Tarski38]A. Tarski, Der Aussagenkalkill und die Topologie, Fund. Math., 31 (1938), pp. 103–134.Google Scholar