Undecidability without arithmetization

被引:34
作者
Grzegorczyk A. [1 ]
机构
[1] 02-055 Warszawa
关键词
Alfred Tarski; Arithmetization; Concatenation; Decidability; Discernibility; Kurt Gödel; Representability;
D O I
10.1007/s11225-005-2976-1
中图分类号
学科分类号
摘要
In the present paper the well-known Gödel's - Church's argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas. © Springer 2005.
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页码:163 / 230
页数:67
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