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Some Remarks on Evaluations of the Primitive Logic
Published online by Cambridge University Press: 22 January 2016
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In [4], K. Ono introduced the notion of evaluations of the primitive logic LO and proved that any semi-evaluation E is an evaluation of LO if E satisfies the following conditions:
(E1) p* → 0 = 0,
(E2) p* → p* = 0,
(E3) 0 → p* = p*,
(E4) p* → (p* → q*) = p* → q*,
(E5) p* → (q* → r*) = q* → (p* → r*),
(E6) p* → q* = 0 implies (r* → p*) → (r* → q*) = 0,
(E7) (x)p*(x) → p*(t) = 0 for any t, and
(E8) if u* → p*(t) = 0 for any t, then u* → (x)p*(x) = 0.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1970
References
[1]
Curry, H., A note on the reduction of Gentzen’s calculus LJ, Bull. Amer. Math. Soc., 45 (1939) 288–293.Google Scholar
[2]
Henkin, L., An algebraic characterization of quantifiers, Fund. Math., 37 (1950) 63–74.Google Scholar
[3]
McKinsey, J.C.C. and Tarski, A., On closed elements in closure algebras, Ann. of Math., 47 (1946) 122–162.Google Scholar
[4]
Ono, K., On a class of truth-value evaluations of the primitive logic, Nagoya Math. J., 31 (1968) 71–80.Google Scholar
[5]
Ono, K., On a class of set-theoretical interpretations of the primitive logic, (to appear).Google Scholar
[6]
Rasiowa, H., Algebraic treatment of the functional calculi of Heyting and Lewis, Fund. Math., 38 (1951) 99–126.CrossRefGoogle Scholar
[7]
Rasiowa, H. and Sikorski, R., The mathematics of metamathematics, Warszawa, 1963, Monografie Maternatyczne tom 41.Google Scholar
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