Evasion and prediction IV: Fragments of constant prediction

常数预测与逃避数，I：推广与变体

Constant prediction and evasion number, I: Generalization and variants

本文将常数逃避概念应用于二元关系，建立了源自已知基数不变量的常数逃避数和常数预测数等新不变量，并给出了相关的极限与一致性结果。

将常规避数和常预测数添加到Cichoń极大模型中

Adding the constant evasion and constant prediction numbers to Cichoń's maximum

本文定义了常规避数$\frak{e}^\textsf{const}_2$和常预测数$\frak{v}_2^\textsf{const}$，并证明二者可被添加到Cichoń极大模型中且取值不同。

Negational Fragment of Intuitionistic Control Logic

We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum. Having two different falsum constants enables to define two forms of negation. We analyse implicational relations between negational monadic formulae and present a poset of non equivalent formulae of this fragment of ICL.

一阶模态逻辑中带非刚性常项和限定摹状词的可判定性

Decidability in First-Order Modal Logic with Non-Rigid Constants and Definite Descriptions

本文系统研究一阶模态逻辑中非刚性常项、限定摹状词和计数特征对可判定性的影响，证明若干一元片段可判定并给出紧致复杂度界，同时指出一种扩展逻辑的Ackermann困难性。

Undecidability of first-order modal and intuitionistic logics with two variables and one monadic predicate letter

We prove that the positive fragment of first-order intuitionistic logic in the language with two variables and a single monadic predicate letter, without constants and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals [QBL, QKC] and [QBL, QFL], where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser's basic and formal logics, respectively. We also show that, for most "natural" first-order modal logics, the two-variable …