Fregean logics with the multiterm deduction theorem and their algebraization

@article{Czelakowski2004FregeanLW,
  title={Fregean logics with the multiterm deduction theorem and their algebraization},
  author={Janusz Czelakowski and Don Pigozzi},
  journal={Studia Logica},
  year={2004},
  volume={78},
  pages={171-212}
}
AbstractA deductive system $$\mathcal{S}$$ (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T, i.e., the binary relation between formulas $$\{ \left\langle {\alpha ,\beta } \right\rangle :T,\alpha \vdash s \beta and T,\beta \vdash s \alpha \} ,$$ is a congruence relation on the formula algebra. The multiterm deduction-detachment theorem is a natural generalization of the deduction theorem of the classical and intuitionistic propositional… 

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