Abstract
The algebra of logic begins with Boole and uses the duality theory for hemimorphisms. This theory largely anticipates Kripke's theory, and in general terms constitutes the main algebraico-topological scheme into which one frequently falls when moving from syntax to semantics and vice versa. The customary transition to Lindenbaum's algebra of a given theory does not usually allow an adequate treatment of diagonal phenomena. The chapter introduces and studies the fixed point algebras. The diagonalizable algebras may be seen as an abstraction of Lindenbaum's P algebra of Peanian arithmetic. The unclear problem of how much of the complex structure of Peanian arithmetic is reproduced in diagonalizable algebra is still open and should give rise to new research on a large scale.
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