Hostname: page-component-7b7567c8c-lpg2g Total loading time: 0 Render date: 2026-11-15T22:55:15.429Z Has data issue: false hasContentIssue false
  • English
  • Français

Free ordered algebraic structures towards proof theory

Published online by Cambridge University Press:  12 March 2014

Andreja Prijatelj
Andreja Prijatelj*
Affiliation:
Department of Mathematics, University of Ljubljana, Slovenia, E-mail: Andreja.Prijatelj@fmf.uni-lj.si
Get accessRights & Permissions [Opens in a new window]

Abstract

In this paper, constructions of free ordered algebras on one generator are given that correspond to some one-variable fragments of affine propositional classical logic and their extensions with n-contraction (n ≥ 2). Moreover, embeddings of the already known infinite free structures into the algebras introduced below are furnished with; thus, solving along the respective cardinality problems.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 2 , June 2001, pp. 597 - 608
Copyright
Copyright © Association for Symbolic Logic 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Birkhoff, G., Lattice Theory, Colloquium Publications, vol. 25, American Mathematical Society, Providence, 1967.Google Scholar
[2]Dean, R. A., Completely Free Lattices Generated by Partially Ordered Sets, Transactions of the American Mathematical Society, vol. 83 (1956), pp. 238–249.CrossRefGoogle Scholar
[3]Freese, R., Ježek, J., and Nation, J. B., Free Lattices, Mathematical Surveys and Monographs, vol. 42, American Mathematical Society, Providence, 1995.CrossRefGoogle Scholar
[4]Girard, J. Y., Linear Logic, Theoretical Computer Science, vol. 50 (1987), pp. 1–101.CrossRefGoogle Scholar
[5]Hori, R., Ono, H., and Schellinx, H., Extending Intuitionistic Linear Logic with Knotted Structural Rules, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 219–242.CrossRefGoogle Scholar
[6]Prijatelj, A., Connectification for n-contraction, Stadia Logica, vol. 54 (1995), pp. 149–171.CrossRefGoogle Scholar
[7]Prijatelj, A., Bounded Contraction and Gentzen-style Formulation of Łukasiewicz Logics, Studia Logica, vol. 57 (1996), pp. 437–456.CrossRefGoogle Scholar
[8]Prijatelj, A., Free Algebras Corresponding to Multiplicative Classical Linear Logic and Some of Its Extensions, Notre Dame Journal of Formal Logic, vol. 37 (1996), pp. 53–70.CrossRefGoogle Scholar
[9]Troelstra, A. S., Lectures on Linear Logic, CSLI Lecture Notes, No 29, Center for the Study of Language and Information, Stanford, 1992.Google Scholar
[10]Whitman, P. M., Free Lattices I and II, Annals of Mathematics, vol. 42 and 43 (1941 and 1942 resp.), pp. 325–330 and 104–105 resp.CrossRefGoogle Scholar