R. C. Lyndon. Relation algebras and projective geometry. The Michigan mathematical journal, vol. 8 (1961), pp. 21–28.

1967 ◽  
Vol 32 (2) ◽  
pp. 275-276
Author(s):  
Thomas Frayne
Keyword(s):  
Projective Geometry ◽  
Mathematical Journal ◽  
Relation Algebras

scholarly journals Undecidable theories of Lyndon algebras

2001 ◽  
Vol 66 (1) ◽  
pp. 207-224 ◽  
Author(s):  
Vera Stebletsova ◽  
Yde Venema
Keyword(s):  
Projective Geometry ◽  
Algebraic Logic ◽  
Equational Theory ◽  
Relation Algebras ◽  
Cylindric Algebras ◽  
Projective Geometries ◽  
Interesting Connection

AbstractWith each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras.

Fuzzy plane projective geometry

1993 ◽  
Vol 54 (2) ◽  
pp. 191-206 ◽  
Author(s):  
K.C. Gupta ◽  
Suryansu Ray
Keyword(s):  
Projective Geometry

scholarly journals Einstein on involutions in projective geometry

2021 ◽  
Author(s):  
Tilman Sauer ◽  
Tobias Schütz
Keyword(s):  
Projective Geometry ◽  
Common Theme ◽  
Infinite Point

AbstractWe discuss Einstein’s knowledge of projective geometry. We show that two pages of Einstein’s Scratch Notebook from around 1912 with geometrical sketches can directly be associated with similar sketches in manuscript pages dating from his Princeton years. By this correspondence, we show that the sketches are all related to a common theme, the discussion of involution in a projective geometry setting with particular emphasis on the infinite point. We offer a conjecture as to the probable purpose of these geometric considerations.

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