论文标题
ikt $^ω$和lukasiewicz-Models
IKT$^ω$ and Łukasiewicz-models
论文作者
论文摘要
在本说明中，我们表明，对于从连续值可估计的olukasiewicz-Models获得的一阶逻辑IK $^ω$，通过将量化器视为无限性强分型/conjunction而不是无限的无限弱分离/结合/结合，用于一阶语言。此外，我们表明，这些模型不能用于为通过以透明的真理扩展IK $^ω$获得的真相IKT $^ω$提供新的一致性证明，因为这些模型与透明的真相不一致。最后，我们表明，是否可以在IKT $^ω$的顺序演算中复制这种不一致取决于对处理的量化方式。
In this note, we show that the first-order logic IK$^ω$ is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKT$^ω$ obtained by expanding IK$^ω$ with transparent truth because the models are inconsistent with transparent truth. Finally, we show that whether or not this inconsistency can be reproduced in the sequent calculus for IKT$^ω$ depends on how vacuous quantification is treated.
