有界马丁最大值与多个证人

Martin's Maximum${}^{\ast, ++}_{\mathfrak{c}}$ in $\mathbb{P}_{\max}$ extensions of strong models of determinacy

We study a strengthening of $\mathrm{MM}^{++}$ which is called $\mathrm{MM}^{\ast, ++}$ and which was introduced by Asperó and Schindler. We force its bounded version $\mathrm{MM}^{\ast, ++}_{\mathfrak{c}}$, which is stronger than both $\mathrm{MM}^{++}(\mathfrak{c})$ as well as $\mathrm{BMM}^{++}$, by $\mathbb{P}_{\max}$ forcing over a determinacy model $L^{F_{\mathrm{uB}}}({\mathbb R}^*,\mbox{Hom}^{\ast})$. The construction of the ground model $L^{F_{\mathrm{uB}}}({\mathbb R}^{\ast},\mbox{Hom}^{\ast})$ builds upon Gappo and Sargsyan, and the derived model construction of Larson, Sargsyan, an…

资源受限的马丁-洛夫类型理论：依赖类型的组合成本分析

Resource-Bounded Martin-Löf Type Theory: Compositional Cost Analysis for Dependent Types

本研究提出一种资源受限的马丁-洛夫类型理论，通过引入资源索引宇宙层级和分级模态，实现对依赖类型的组合成本分析，并通过案例研究展示其在认证算法成本界限方面的应用。

BMM比BSPFA强

BMM is stronger than BSPFA

它表明，如果BMM（=有界马丁的最大值）举行，然后每个集包含在一个内部模型具有强基数。这回答了许多人提出的一个问题。由此可见，BMM比BSPFA（Bounded Semi-proper Forcing Axiom）具有更大的一致性强度。