逻辑/信息论学术速递[1.10]
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math.LO逻辑，共计3篇
math.IT信息论，共计0篇
1.math.LO逻辑:
【1】 TOWER-Complete Problems in Contraction-Free Substructural Logics
标题：无收缩子结构逻辑中的塔式完备性问题
链接：https://arxiv.org/abs/2201.02496
备注：Draft
摘要：We investigate the computational complexity of a family of substructural
logics with exchange and weakening but without contraction. With the aid of the
techniques provided by Lazi\'c and Schmitz (2015), we show that the
deducibility problem for full Lambek calculus with exchange and weakening
($\mathbf{FL}_{\mathbf{ew}}$) is TOWER-complete, where TOWER is one of the
non-elementary complexity classes introduced by Schmitz (2016). The same
complexity result holds even for deducibility in BCK-logic, i.e., the
implicational fragment of $\mathbf{FL}_{\mathbf{ew}}$. We furthermore show the
TOWER-completeness of the provability problem for elementary affine logic,
which was proved to be decidable by Dal Lago and Martini (2004).
【2】 The extent of saturation of induced ideals
标题：诱导理想的饱和程度
链接：https://arxiv.org/abs/2201.02364
摘要：We construct a model with a saturated ideal $I$ over
$\mathcal{P}_{\kappa}\lambda$ and study the extent of saturation of $I$.
【3】 Prikry-type forcing and the set of possible cofinalities
标题：Prikry型强迫与可能余定集
链接：https://arxiv.org/abs/2201.02322
摘要：It is known that the set of possible cofinalities $\mathrm{pcf}(A)$ has good
properties if $A$ is a progressive interval of regular cardinals. In this
paper, we give an interval of regular cardinals $A$ such that $\mathrm{pcf}(A)$
has no good properties in the presense of a measurable cardinal, or in generic
extensions by Prikry-type forcing.
2.math.IT信息论:
机器翻译，仅供参考
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