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Free L-algebras1

Published online by Cambridge University Press:  12 March 2014

Alfred Horn
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Extract

Dummett's LC [1] is a system which characterizes all formulas of the propositional calculus which are valid in every chain (for definitions and notation see the first section of [2]). An L-algebra is a Heyting algebra in which (x → y) + (y → x) = 1 for all x, y. L-algebras bear the same relation to LC as Boolean algebras to the classical propositional calculus and Heyting algebras to the intuitionist propositional calculus.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 475 - 480
Copyright
Copyright © Association for Symbolic Logic 1969

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Footnotes

1

This research was supported in part by National Science Foundation Grant No. 5600.

References

[1]Dummett, M., A propositional calculus with denumerable matrix, this Journal, vol. 24 (1959), pp. 97–106.Google Scholar
[2]Horn, A., Logic with truth values in a linearly ordered Heyting algebra, this Journal vol. 34 (1969), pp. 395–408.Google Scholar