One of the Possible Formal Desribtions of Deducubility

Branislav R. Boričić

Publications de l'Institut Mathématique, _N_S_34 (1983) no. 48, p. 13

Résumé

Having in mind different investigations of implication, i.e., of the logical consequence relation, we will try to point out a general kernel of formal systems in which the deducibility relation is stated in the system itself. In connection with any formal theory $\theta$ we observe a formal theory $\theta(\to)$ which is able to define the fundamental factor of $\theta$-{\it deducibility}. By showing that the basic binary relation of $\theta(\to)$ is just a formal description of the metatheoretic deducibility relation of $\theta$, the essential statement, the assertion 2.9., justifies contemplation of a formal theory like $\theta(\to)$. Furthermore, by the assertions 3.3 and 3.4 an interesting conection between formal theories $\theta(\sim)$ (cf~[1]) and $\theta(\to)$ is given.

Détail

Classification : 03B05 03G25