{"name": "数理逻辑・数学基础", "children": [{"name": "数学基础", "children": [{"name": "公理化理论", "en": "axiomatic theory", "superfield": "数学"}, {"name": "公理学", "en": "axiomatics", "superfield": "数学"}, {"name": "实无穷", "en": "actual infinity", "superfield": "数学"}, {"name": "有限论者", "en": "finitist", "superfield": "数学"}, {"name": "潜无穷", "en": "potential infinity", "superfield": "数学"}, {"name": "直谓[的]", "en": "predicative", "superfield": "数学"}, {"name": "逻辑主义", "en": "logicism", "superfield": "数学"}, {"name": "非形式公理学", "en": "informal axiomatics", "superfield": "数学"}, {"name": "非直谓[的]", "en": "impredicative", "superfield": "数学"}]}, {"name": "模型论", "children": [{"name": "一阶理论", "en": "first-order theory", "superfield": "数学"}, {"name": "一阶逻辑", "en": "first-order logic", "superfield": "数学"}, {"name": "万有模型", "en": "universal model", "superfield": "数学"}, {"name": "不可辨元", "en": "indiscernible", "superfield": "数学"}, {"name": "个体变元", "en": "individual variable", "superfield": "数学"}, {"name": "互斥析取", "en": "exclusive disjunction", "superfield": "数学"}, {"name": "代入", "en": "substitution", "superfield": "数学"}, {"name": "假值", "en": "falsity", "superfield": "数学"}, {"name": "全域", "en": "universe", "superfield": "数学"}, {"name": "全称量词", "en": "universal quantifier", "superfield": "数学"}, {"name": "内插定理", "en": "interpolation theorem", "superfield": "数学"}, {"name": "出现", "en": "occurrence", "superfield": "数学"}, {"name": "函数符号", "en": "function symbol", "superfield": "数学"}, {"name": "初等子模型", "en": "elementary submodel", "superfield": "数学"}, {"name": "初等子结构", "en": "elementary substructure", "superfield": "数学"}, {"name": "初等等价[的]", "en": "elementarily equivalent", "superfield": "数学"}, {"name": "前束范式", "en": "prenex normal form", "superfield": "数学"}, {"name": "前束词", "en": "prefix", "superfield": "数学"}, {"name": "原子[语]句", "en": "atomic sentence", "superfield": "数学"}, {"name": "原子公式", "en": "atomic formula", "superfield": "数学"}]}, {"name": "证明论", "children": [{"name": "ω相容性", "en": "ω-consistency", "superfield": "数学"}, {"name": "不可证明性", "en": "unprovability", "superfield": "数学"}, {"name": "二阶算术", "en": "second-order arithmetic", "superfield": "数学"}, {"name": "佩亚诺公理", "en": "Peano axiom", "superfield": "数学"}, {"name": "元逻辑", "en": "metalogic", "superfield": "数学"}, {"name": "判定问题", "en": "decision problem", "superfield": "数学"}, {"name": "可判定性", "en": "decidability", "superfield": "数学"}, {"name": "可驳[的]", "en": "refutable", "superfield": "数学"}, {"name": "希尔伯特计划", "en": "Hilbert program", "superfield": "数学"}, {"name": "形式不可判定命题", "en": "formal undecidable proposition", "superfield": "数学"}, {"name": "截规则", "en": "cut rule", "superfield": "数学"}, {"name": "抽象[化]", "en": "abstraction", "superfield": "数学"}, {"name": "数词可表示性", "en": "numeralwise representability", "superfield": "数学"}, {"name": "构造性", "en": "constructivity", "superfield": "数学"}, {"name": "构造论者", "en": "constructivist", "superfield": "数学"}, {"name": "独立性", "en": "independence", "superfield": "数学"}, {"name": "直觉主义数学", "en": "intuitionistic mathematics", "superfield": "数学"}, {"name": "相对相容性", "en": "relative consistency", "superfield": "数学"}, {"name": "算术化", "en": "arithmetization", "superfield": "数学"}, {"name": "算术系统", "en": "arithmetic system", "superfield": "数学"}]}, {"name": "递归论", "children": [{"name": "NP问题", "en": "NP problem", "superfield": "数学"}, {"name": "α有限", "en": "α-finite", "superfield": "数学"}, {"name": "α递归性", "en": "α-recursion", "superfield": "数学"}, {"name": "λ可定义函数", "en": "λ-definable function", "superfield": "数学"}, {"name": "λ演算", "en": "λ-calculus", "superfield": "数学"}, {"name": "μ算子", "en": "μ-operator", "superfield": "数学"}, {"name": "一一可归约性", "en": "one-one reducibility", "superfield": "数学"}, {"name": "不可解性", "en": "unsolvability", "superfield": "数学"}, {"name": "丘奇论题", "en": "Church thesis", "superfield": "数学"}, {"name": "丢番图关系", "en": "Diophantine relation", "superfield": "数学"}, {"name": "优先[方]法", "en": "priority method", "superfield": "数学"}, {"name": "停机问题", "en": "halting problem", "superfield": "数学"}, {"name": "创造集", "en": "creative set", "superfield": "数学"}, {"name": "加速", "en": "speedup", "superfield": "数学"}, {"name": "单[纯]集", "en": "simple set", "superfield": "数学"}, {"name": "博雷尔分层", "en": "Borel hierarchy", "superfield": "数学"}, {"name": "原始递归式", "en": "primitive recursion", "superfield": "数学"}, {"name": "原始递归性", "en": "primitive recursiveness", "superfield": "数学"}, {"name": "及时单纯集", "en": "promptly simple set", "superfield": "数学"}, {"name": "可归约[的]", "en": "reducible", "superfield": "数学"}]}, {"name": "集合论", "children": [{"name": "0#", "en": "zero-sharp", "superfield": "数学"}, {"name": "0+", "en": "zero-dagger", "superfield": "数学"}, {"name": "不可达基数", "en": "inaccessible cardinal", "superfield": "数学"}, {"name": "世传可数[的]", "en": "hereditarily countable", "superfield": "数学"}, {"name": "世传有穷集", "en": "hereditarily finite set", "superfield": "数学"}, {"name": "佐恩引理", "en": "Zorn lemma", "superfield": "数学"}, {"name": "公理化集合论", "en": "axiomatic set theory", "superfield": "数学"}, {"name": "共尾子集", "en": "cofinal subset", "superfield": "数学"}, {"name": "共尾性", "en": "cofinality", "superfield": "数学"}, {"name": "分支类型论", "en": "ramified theory of types", "superfield": "数学"}, {"name": "初始序数", "en": "initial ordinal", "superfield": "数学"}, {"name": "初始段", "en": "initial segment", "superfield": "数学"}, {"name": "初步集[合]", "en": "rudimentary set", "superfield": "数学"}, {"name": "力迫关系", "en": "forcing relation", "superfield": "数学"}, {"name": "力迫条件", "en": "forcing condition", "superfield": "数学"}, {"name": "力迫法", "en": "forcing method", "superfield": "数学"}, {"name": "可构成[的]", "en": "constructible", "superfield": "数学"}, {"name": "可构成壳", "en": "constructible hull", "superfield": "数学"}, {"name": "可构成性", "en": "constructibility", "superfield": "数学"}, {"name": "可测基数", "en": "measurable cardinal", "superfield": "数学"}]}, {"name": "非经典逻辑", "children": [{"name": "多值逻辑", "en": "multivalue logic", "superfield": "数学"}, {"name": "拓扑逻辑", "en": "topological logic", "superfield": "数学"}, {"name": "概率逻辑", "en": "probability logic", "superfield": "数学"}, {"name": "模态逻辑", "en": "modal logic", "superfield": "数学"}, {"name": "组合逻辑", "en": "combinatory logic", "superfield": "数学"}, {"name": "范畴逻辑", "en": "categorical logic", "superfield": "数学"}]}]}