## The Journal of Symbolic Logic, Volumes 9-12Vol. 1, no. 4 (Dec. 1936) consists of a bibliography of symbolic logic for the period 1666-1935, by Alonzo Church (with additions and corrections in v. 3, no. 4). |

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Page 102

We find here in particular a logistic treatment of the propositional calculus in

nearly its modern form, an analysis of the use of variables, the

propositional function, the use of quantifiers, the explicit statement of primitive

rules of inference, the

proof by mathematical induction. 2. The author brings forward once more an old

criticism of Frege's definition of the number of a concept F (as the extension of the

concept similar to ...

We find here in particular a logistic treatment of the propositional calculus in

nearly its modern form, an analysis of the use of variables, the

**notion**ofpropositional function, the use of quantifiers, the explicit statement of primitive

rules of inference, the

**notion**of an hereditary property and the logical analysis ofproof by mathematical induction. 2. The author brings forward once more an old

criticism of Frege's definition of the number of a concept F (as the extension of the

concept similar to ...

Page 109

1945 ON THE INTERPRETATION OF INTUITIONISTIC NUMBER THEORY B. C.

KLEENE The purpose of this article is to introduce the

- bility."1 1. Let P be some property of natural numbers. Consider the existential

statement, "There exists a number n having the property P." To explain the

meaning which this has for a constructivist or intuitionist, it has been described as

a partial judgement, or incomplete communication of a more specific statement

which ...

1945 ON THE INTERPRETATION OF INTUITIONISTIC NUMBER THEORY B. C.

KLEENE The purpose of this article is to introduce the

**notion**of "recursive realiza- bility."1 1. Let P be some property of natural numbers. Consider the existential

statement, "There exists a number n having the property P." To explain the

meaning which this has for a constructivist or intuitionist, it has been described as

a partial judgement, or incomplete communication of a more specific statement

which ...

Page 115

The author's earlier conjecture in this direction was expressed in terms of the

recursively fulfillable, if there exists a general recursive function iA(xi,- □ •>*»)

such that, for every set xi, □ □ • ,x„ of natural numbers, the formula B(xi, • • • ,xn,y

), where y = ^-(av • - ,xn), is true. The present results in terms of recursive

realizability are of more interest, since the

to formulas of the ...

The author's earlier conjecture in this direction was expressed in terms of the

**notion**of "recursive fulfillability":11 the formula Vxi • • • Vx„3yB(xi, • • • ,x«,y) isrecursively fulfillable, if there exists a general recursive function iA(xi,- □ •>*»)

such that, for every set xi, □ □ • ,x„ of natural numbers, the formula B(xi, • • • ,xn,y

), where y = ^-(av • - ,xn), is true. The present results in terms of recursive

realizability are of more interest, since the

**notion**of recursive fulfillability is limitedto formulas of the ...

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### Contents

TABLE OF CONTENTS | 108 |

A set of axioms for logic By Theodore Hailperin 1 | 143 |

All numbers of this volume are copyrighted by the Association for Symbolic Logic | 60 |

2 other sections not shown

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### Common terms and phrases

Alonzo Church alternative denial Andrzej Mostowski applied arguments Association for Symbolic Avenue axiomatic axioms Boolean algebra Brouwerian algebra California Carnap classical closure algebra College concepts concrete consists constructed contains no free defined definition elements existence expressions finite follows formal formula free variables given Godel Hence Ibid Illinois implication individual induction inscription interpretation intuitionistic Jersey Journal Lemma lines logique LPar m-valued propositional Massachusetts Max Black means method modal Moore-Osgood theorem natural numbers negation Nelson nominalistic notation notion number theory object language ordered pair paper parentheses philosophy possible postulates primitive recursive Princeton principle problem Prof proof propositional calculus provable prove quantifiers realizable recursive functions reference relation result reviewer rule of inference semantics sense sentence sequence statement Street substitution Symbolic Logic syntax Tarski tion trois valeurs true truth truth-value University values W. V. Quine York