## Journal of Symbolic Logic

### Deduction Theorems within RM and Its Extensions

#### Abstract

In [13], M. Tokarz specified some infinite family of consequence operations among all ones associated with the relevant logic RM or with the extensions of RM and proved that each of them admits a deduction theorem scheme. In this paper, we show that the family is complete in a sense that if C is a consequence operation with $C_{RM} \leq C$ and C admits a deduction theorem scheme, then C is equal to a consequence operation specified in [13]. In algebraic terms, this means that the only quasivarieties of Sugihara algebras with the relative congruence extension property are the quasivarieties corresponding, via the algebraization process, to the consequence operations specified in [13].

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 1 (1999), 279-290.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745705

Mathematical Reviews number (MathSciNet)
MR1683908

Zentralblatt MATH identifier
0967.03015

JSTOR
links.jstor.org

#### Citation

Czelakowski, J.; Dziobiak, W. Deduction Theorems within RM and Its Extensions. J. Symbolic Logic 64 (1999), no. 1, 279--290. https://projecteuclid.org/euclid.jsl/1183745705