Boolean products of lattices

A study is made of Boolean product representations of bounded lattices over the Stone space of their centres. Special emphasis is placed on relating topological properties such as clopen or regular open equalizers to their equivalent lattice theoretic counterparts. Results are also presented connecting various properties of a lattice with properties of its individual stalks.

[1]  Roberto Cignoli,et al.  The lattice of global sections of sheaves of chains over Boolean spaces , 1978 .

[2]  Brian A. Davey,et al.  Sheaf spaces and sheaves of universal algebras , 1973 .

[3]  Fumitomo Maeda,et al.  Theory of symmetric lattices , 1970 .

[4]  G. Birkhoff.  Subdirect unions in universal algebra , 1944 .

[5]  John Dauns,et al.  The representation of biregular rings by sheaves , 1966 .

[6]  Stanley Burris,et al.  A course in universal algebra , 1981, Graduate texts in mathematics.

[7]  Bernhard Banaschewski,et al.  Hüllensysteme und Erweiterung von Quasi‐Ordnungen , 1956 .

[8]  M. Janowitz.  Note on the center of a lattice , 1978 .

[9]  John Harding,et al.  Completions of orthomodular lattices , 1990 .

[10]  W. Burgess,et al.  Pierce sheaves of non-commutative rings , 1976 .

[11]  Roberto Cignoli,et al.  Representation of Łukasiewicz and Post algebras by continuous functions , 1972 .

[12]  S. Burris,et al.  Sheaf constructions and their elementary properties , 1979 .

[13]  A Bundle Representation for Continuous Geometries , 1997 .

[14]  M. Stone,et al.  The Theory of Representation for Boolean Algebras , 1936 .

[15]  R. Kopperman.  Model theory and its applications , 1972 .

[16]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[17]  G. Epstein.  The lattice theory of Post algebras , 1960 .

[18]  M. Stone.  The theory of representations for Boolean algebras , 1936 .

[19]  H. M. Macneille,et al.  Partially ordered sets , 1937 .

[20]  S. D. Comer,et al.  Representations by algebras of sections over Boolean spaces. , 1971 .

[21]  R. P. Dilworth.  Lattices with Unique Complements , 1945 .

[22]  Completions of orthomodular lattices II , 1993 .

[23]  George Epstein,et al.  Logics Which Are Characterized by Subresiduated Lattices , 1976, Math. Log. Q..

[24]  R. Pierce.  Modules over Commutative Regular Rings , 1967 .

[25]  Angus Macintyre.  Model-completeness for sheaves of structures , 1973 .

[26]  George Epstein,et al.  P-Algebras, an abstraction from Post algebras , 1974 .