Maurice L'Abbé. On the independence of Henkin's axioms for fragments of the propositional calculus. The journal of symbolic logic, vol. 16 (1951) pp. 43–45.

1951 ◽  
Vol 16 (3) ◽  
pp. 228-228
Author(s):  
Sören Halldén
Keyword(s):  
Propositional Calculus ◽  
Symbolic Logic

A system of implicit quantification

1968 ◽  
Vol 32 (4) ◽  
pp. 480-504 ◽  
Author(s):  
J. Jay Zeman
Keyword(s):  
Subject Matter ◽  
Traditional Method ◽  
Natural Deduction ◽  
Propositional Calculus ◽  
Axiom System ◽  
Symbolic Logic ◽  
Quantification Theory ◽  
The Subject

The “traditional” method of presenting the subject-matter of symbolic logic involves setting down, first of all, a basis for a propositional calculus—which basis might be a system of natural deduction, an axiom system, or a rule concerning tautologous formulas. The next step, ordinarily, consists of the introduction of quantifiers into the symbol-set of the system, and the stating of axioms or rules for quantification. In this paper I shall propose a system somewhat different from the ordinary; this system has rules for quantification and is, indeed, equivalent to classical quantification theory. It departs from the usual, however, in that it has no primitive quantifiers.

Logical works, by Mordchaj Wajsberg. Edited and with an introduction by Stanisław J. Surma. ZakВad Narodowy imienia Ossolińskich, Wydawnictwo Polskiej Akademii Nauk, Wrocław etc. 1977, 216 pp. - Stanisław J. Surma. Mordchaj Wajsberg. Life and work. Pp. 7–11. - Mordchaj Wajsberg. Axiomatization of the three-valued propositional calculus. Pp. 12–29. A reprint of XXXV 442(15) (English translation by B. Gruchman and S. McCall of 4371). - Mordchaj Wajsberg. On the axiom system of propositional calculus. Pp. 30–36. English translation of 4372. - Mordchaj Wajsberg. A new axiom of propositional calculus in Sheffer's sbmbols. Pp. 37–39. English translation of 4373. - Mordchaj Wajsberg. Investigations of functional calculus for finite domain of individuals. Pp. 40–49. English translation of 4374. - Mordchaj Wajsberg. An extended class calculus. Pp. 50–61. English translation of 4375. - Mordchaj Wajsberg. A contribution to metamathematics. Pp. 62–88. English translation of 4376. - Mordchaj Wajsberg. Contributions to meta-calculus of propositions I. Pp. 89–106. English translation of 4377. - Mordchaj Wajsberg. On the matrix method of independence proofs. Pp. 107–131. English translation of I 75. - Mordchaj Wajsberg. On A. Heyting's propositional calculus. Pp. 132–171. English translation of III 169. - Mordchaj Wajsberg. Contributions to metalogic. Pp. 172–200. Areprint of XXXV 442(16) (English translation by S. McCall and P. Woodruff of II 93). - Mordchaj Wajsberg. Contributions to metalogic II. Pp. 201–214. A reprint of XXXV 442(17) (English translation by S. McCall of V 31). - Mordchaj Wajsberg. Review of Mihailescu's Recherches sur les formes normalespar rapport à l'equivalence et la disjonction, dans le calcul des propositions (IV 91). Pp. 215–216. English translation of pp. 91–92 of The journal of symbolic logic, vol. 4 (1939).

1983 ◽  
Vol 48 (3) ◽  
pp. 873-874
Author(s):  
Storrs McCall
Keyword(s):  
English Translation ◽  
Functional Calculus ◽  
Matrix Method ◽  
Propositional Calculus ◽  
Axiom System ◽  
Finite Domain ◽  
Symbolic Logic ◽  
The Matrix ◽  
Extended Class
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