Journal of Symbolic Logic

Finitely generated free Heyting algebras: the well-founded initial segment

R. Elageili and J. K. Truss

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In this paper we describe the well-founded initial segment of the free Heyting algebra ${\mathbb A}_\alpha$ on finitely many, $\alpha$, generators. We give a complete classification of initial sublattices of ${\mathbb A}_2$ isomorphic to ${\mathbb A}_1$ (called ‘low ladders'), and prove that for $2 \le \alpha < \omega$, the height of the well-founded initial segment of ${\mathbb A}_\alpha$ is $\omega^2$.

Article information

J. Symbolic Logic, Volume 77, Issue 4 (2012), 1291-1307.

First available in Project Euclid: 15 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03G25: Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] 06D20: Heyting algebras [See also 03G25]

free Heyting algebra well-founded low ladder


Elageili, R.; Truss, J. K. Finitely generated free Heyting algebras: the well-founded initial segment. J. Symbolic Logic 77 (2012), no. 4, 1291--1307. doi:10.2178/jsl.7704140.

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