Frederic B. Fitch. The Heine-Borel theorem in extended basic logic. The journal of symbolic logic, vol. 14 (1949), pp. 9–15.

1950 ◽  
Vol 15 (2) ◽  
pp. 137-137
Author(s):  
S. C. Kleene
Keyword(s):  
Symbolic Logic ◽  
Basic Logic

An extensional variety of extended basic logic

1958 ◽  
Vol 23 (1) ◽  
pp. 13-21 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Mathematical Analysis ◽  
Symbolic Logic ◽  
Basic Logic ◽  
Natural Numbers ◽  
Strong Principle ◽  
Theory Of Numbers

The system K′ of “extended basic logic” lacks a principle of extensionality. In this paper a system KE′ will be presented which is like K′ in many respects but which does possess a fairly strong principle of extensionality by way of rule 6.37 below. It will be shown that KE′ is free from contradiction. KE′ is especially well suited for formalizing the theory of numbers presented in my paper, On natural numbers, integers, and rationals. The methods used there can be applied even more directly here because of the freedom of KE′ from type restrictions, but the details of such a derivation of a portion of mathematics will not be presented in this paper. It is evident, moreover, that KE′ contains at least as much of mathematical analysis as does K′, and perhaps considerably more. The method of carrying out proofs in KE′ is closely similar to that used in my book Symbolic logic, and could be expressed in similar notation.

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