Does Anyone Have the Blue Files Book?

103 命 Destiny's Azure Files Drinking Tea and Fishing741k WordsOngoing 783Reads—Score115Shelves

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Recommend your own book; it is a cool novel with no knives and multiple female protagonists; the emotional scenes are not complicated, and there is no random plot, and the daily plot is full of sugar; the plot is not brainless, does not copy the main line of the game, and the original plot is sufficient - where does the "halo" above the students' heads originate? How does the Federal Student Union fully take over Caesars Group? How did the Treaty of Eden, which originally had its own ulterior motives, turn into a perfect trap jointly set by the three parties for Arius with the intervention of the protagonist? And... How is the science fiction setting of Destiny 2 connected with the world view of Azure Files? I don't know if you can enjoy reading it, but the author can guarantee one thing - this is definitely a different story.

104 B One Week of BA, I Have Super Powers I Dream of Dawn394k WordsCompleted 1.4kReads7.1Score212Shelves

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There is always someone you like

105 蔚 Azure Files: I'm a Little Too Popular Ship's Companion373k WordsCompleted 2.4kReads7.5Score333Shelves

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It's all here

107 蔚 When Wei Lan Is Reliable, It Is Very Reliable. When It Is Not Reliable, It Is Ridiculous. KONO Philosophy612k WordsOngoing 2.3kReads8.2Score308Shelves

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These two are beautiful.

113 万 Ten Thousand Demons Hall Councilor's Splitting Power Wei Xuli204k WordsOngoing 549Reads—Score110Shelves

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It's more of a daily routine. Iroha is a single heroine. She's not included in the main plot for the time being. In the future, it will be slightly integrated with the Honsan worldview (go to Honsan). If you have any suggestions, the author will listen to them. Then read Volume 2 first and then Volume 1. There is no traffic for children.

120 蔚 Blue Files: the Truth About the World Xiaoyu Xianguancao294k WordsOngoing 31Reads—Score—Shelves

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Aren't you curious about this name and introduction? ?

122 蔚 Blue Files: Stars Fall, New Stars Rise Tiger and Tiger Show Off Their Power229k WordsOngoing 522Reads6.5Score—Shelves

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I'm giving you a box about outer second lines, no need to thank me. 1. Ordinal stacking (the transition of complexity within countable infinity) 1. Finite ordinal numbers: 0, 1, 2, ... 2. Transfinite ordinal numbers: - ω (the first infinite ordinal number)→ω+1→ω·2→ω²→ε₀=φ(1,0) (the first ε ordinal number) - Veblen function: φ(1,1), φ(2,0)=ζ₀, φ(ω,0)→Γ₀=φ(1,0,0) (Fefferman-Schute number) - Large recursion ordinal: SVO (small Veblen number) → LVO (large Veblen number) → BHO (Bachmann-Howard number) 3. Essential limit: All recursive ordinal numbers are <ω₁^CK (Church-Kleene ordinal numbers) and are countable ordinal numbers (|ω₁^CK|=ℵ₀). 2. Cardinal stacking (breaking through the potential level of countability) 1. Driven by the power set axiom: - ℵ₀→ℵ₁=2^ℵ₀→ℵ₂→…→ℵ_ω (the first singular cardinal number) 2. Fixed point transition: - ℵ_{ℵ₀}→ℵ_{ℵ_{ℵ₀}}→…→Aleph fixed point κ=ℵ_κ - higher-order fixed point: αth fixed point→fixed point of fixed point→… 3. Essential limitation: This path is still within the definable range of ZFC (need to assume the power set axiom). 3. Large cardinality axiom (beyond the absolute infinity of ZFC) Strength index: If the cardinality κ exists, the consistency strength of ZFC + "κ exists" is strictly greater than ZFC. - Unreachable cardinals: regular strong limit cardinals (∀λ<κ, 2^λ<κ), which are the first ZFC independent axioms beyond the ℵ fixed point. - Marlowe cardinal numbers: unreachable cardinal numbers "reside" under κ, introducing higher-order regularity. - Weakly compact cardinality: satisfies κ→(κ)²₂ or Π¹₁-indescribable, and is associated with combinatorial properties and logical compactness. - Measurable cardinality: The existence of κ-complete non-primary ultrafilters is the starting point of elementary embedding theory. - Strong cardinality: There is an elementary embedding j: V→M, so that V_λ⊆M (λ is arbitrarily large), breaking through the closure of the local model. - Woodin base: For any A⊆V_κ, there is an elementary embedding that preserves A, which is deeply related to the determinacy axiom (AD). - Super strong base: satisfies V_{j(κ)}⊆M, the closure of j(κ) is stronger than the strong base. - Ultracompact cardinality: for any λ ≥ κ, there exists a λ-ultrafilter, which is a key goal of the inner model scheme. - N-huge cardinality: satisfies ^{j^n(κ)}M⊆M, reflecting iterative embedding closure. - Berkeley cardinality: For any transfer model M containing κ, there exists j: M→M, transcending Kunen inconsistency (the ZF regularity axiom needs to be abandoned). 4. The ultimate structure of the collective universe 1. Von Neumann universe V: - Structure: V₀=∅, V_{α+1}=℘(Vₐ), V=⋃_{α∈Ord}Vₐ. - Properties: V is the expected global model of ZFC, and large cardinality exists in high-level V_κ. 2. Gödel can construct the universe L: - Construction: L₀=∅, L_{α+1}=Def(Lₐ), L=⋃_{α∈Ord}Lₐ. - Defect: L excludes measurable cardinals and large cardinals above (L⊨ "¬∃ measurable cardinal"). 3. Ultimate-L conjecture: - Goal: Construct an intra-canonical model U⊆V that accommodates all known large cardinalities. - Axiomatic requirements: U⊨GCH+strong Ω-conjecture; U compatible with ultra-compact/huge cardinalities; V=Ultimate-L (inevitable under Ω-logic). - Significance: If established, the continuum hypothesis (CH) can be solved and set theory unified. 5. Beyond V: Multiverse and Consistency Boundary 1. Forcing: Add "generic set G" to V through the partially ordered set ℙ to construct the expanded universe V[G]. For example, Cohen force can make V[G]⊨2^ℵ₀=ℵ₂. 2. Set theory multiverse (Multiverse): - Axiomatic framework (Hamkins): All forced expansions V[G] are equal universes. - Philosophical proposition: monism believes that V is the only absolute universe (supporter of ultimate L); pluralism believes that there are infinitely many ZFC universes (supporter of force-forcing method). 3. Ultimate bound: - Kunen inconsistency: There is no non-trivial elementary embedding j: V→V in ZFC. - Consistency limit: Above the Berkeley cardinality, ZF axioms (such as regularity axioms) need to be sacrificed. The essence of mathematical stacking and the hierarchical pyramid (1) Consistency strength level (from low to high) Recursive ordinal (BHO) < unreachable cardinality < measurable cardinality < Woodin cardinality < ultra-compact cardinality < n-huge cardinality < Berkeley cardinality Note: The intensity of each level increases strictly, and the higher-level axioms imply the consistency of the lower-level axioms. (2) The core mechanism of stacking - recursive definition: the transition of ω→ε₀→Γ₀→BHO is achieved through ordinal functions (Veblen, OCF). - Power set axiom: drives the base expansion ℵₙ→ℵₙ₊₁, such as ℵ₀→ℵ₁→ℵ_ω. - Fixed point: satisfies κ=F(κ) (F is a hierarchical function), such as Aleph fixed point → Marlowe number. - Elementary embedding: jump from measurable cardinality to super strong cardinality through non-trivial embedding of j: V→M. - Inner model planning: construct extensions of L (e. G. L[U]→L[E→]→ultimate L) to accommodate large cardinal numbers.

125 蔚 Azure Files: Feathers of Rebirth Mo Yuming83k WordsOngoing 317Reads5.8Score—Shelves

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There is also a highly recommended book called "Becoming Hina's Little Brother"

135 绯 Crimson Archives: Provence Ye Qing881k WordsOngoing 312Reads8.7Score—Shelves

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The plot is in-depth, the adaptation is thorough, the behavior is abstract, and the summary is really nice. The author is currently updating another book instead of this one.

137 重 Reborn as a Student of Abydos? Seyu225k WordsOngoing 1Reads5.8Score—Shelves

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Please recommend yourself

138 B BA: I'm Going to Play Kasuga Shadow in Kivo Too! Alice's Feet Smell Good235k WordsOngoing 3kReads7.0Score605Shelves

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All very good

139 蔚 Blue Archives: Blue Reverberation's Daily Life in Kiwo Light Script Written by Ayin157k WordsOngoing 247Reads6.4Score—Shelves

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He! Heavy! New! Even! New! Got it! !

144 蔚 Cerulean Punk: Cyber ​​Archives Lwvvvvv389k WordsOngoing 1Reads5.8Score—Shelves

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[Sending Hearts][Sending Hearts] This new work derived from the Blue Files is very beautiful. It is a great book both in terms of the sense of immersion and the plot setting. 🌈The rhythm is strong, non-toxic, and the foreshadowing and reversal are constant. I must recommend this good book.

145 蔚 Blue File IF: the Imbalanced Balance of Mirroring Leave No Space Blank63k WordsOngoing 3Reads—Score—Shelves

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If you push yourself a bit, can you become a streamer?

148 蔚 Azure Files: There Is a Little Fox at the End of the Windy Sand It's Wanyue165k WordsCompleted 334Reads—Score—Shelves

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I would like to recommend what I wrote. The first book is a healing text, and the second book is a depression text [laughing]

149 B BA: Senior of SRT Rabbit Team God Knows the World620k WordsOngoing 1.3kReads6.8Score158Shelves

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I'm giving you a box about outer second lines, no need to thank me. 1. Ordinal stacking (complexity transition within countable infinity) 1. Finite ordinal numbers: 0, 1, 2, ... 2. Transfinite ordinal numbers: - ω (the first infinite ordinal number)→ω+1→ω·2→ω²→ε₀=φ(1,0) (the first ε ordinal number) - Veblen function: φ(1,1), φ(2,0)=ζ₀, φ(ω,0)→Γ₀=φ(1,0,0) (Fefferman-Schute number) - Large recursion ordinal: SVO (small Veblen number) → LVO (large Veblen number) → BHO (Bachmann-Howard number) 3. Essential limit: All recursive ordinal numbers are <ω₁^CK (Church-Kleene ordinal numbers) and are countable ordinal numbers (|ω₁^CK|=ℵ₀). 2. Cardinal stacking (breaking through the potential level of countability) 1. Driven by the power set axiom: - ℵ₀→ℵ₁=2^ℵ₀→ℵ₂→…→ℵ_ω (the first singular cardinal number) 2. Fixed point transition: - ℵ_{ℵ₀}→ℵ_{ℵ_{ℵ₀}}→…→Aleph fixed point κ=ℵ_κ - higher-order fixed point: αth fixed point→fixed point of fixed point→… 3. Essential limitation: This path is still within the definable range of ZFC (need to assume the power set axiom). 3. Large cardinality axiom (beyond the absolute infinity of ZFC) Strength index: If the cardinality κ exists, the consistency strength of ZFC + "κ exists" is strictly greater than ZFC. - Unreachable cardinals: regular strong limit cardinals (∀λ<κ, 2^λ<κ), which are the first ZFC independent axioms beyond the ℵ fixed point. - Marlowe cardinal numbers: unreachable cardinal numbers "reside" under κ, introducing higher-order regularity. - Weakly compact cardinality: satisfies κ→(κ)²₂ or Π¹₁-indescribable, and is associated with combinatorial properties and logical compactness. - Measurable cardinality: The existence of κ-complete non-primary ultrafilters is the starting point of elementary embedding theory. - Strong cardinality: There is an elementary embedding j: V→M, so that V_λ⊆M (λ is arbitrarily large), breaking through the closure of the local model. - Woodin base: For any A⊆V_κ, there is an elementary embedding that preserves A, which is deeply related to the deterministic axiom (AD). - Super strong base: satisfies V_{j(κ)}⊆M, the closure of j(κ) is stronger than the strong base. - Ultracompact cardinality: for any λ ≥ κ, there exists a λ-ultrafilter, which is a key goal of the inner model scheme. - N-huge cardinality: satisfies ^{j^n(κ)}M⊆M, reflecting iterative embedding closure. - Berkeley cardinality: For any transfer model M containing κ, there exists j: M→M, transcending Kunen inconsistency (the ZF regularity axiom needs to be abandoned). 4. The ultimate structure of the collective universe 1. Von Neumann universe V: - Structure: V₀=∅, V_{α+1}=℘(Vₐ), V=⋃_{α∈Ord}Vₐ. - Properties: V is the expected global model of ZFC, and large cardinality exists in high-level V_κ. 2. Gödel can construct the universe L: - Construction: L₀=∅, L_{α+1}=Def(Lₐ), L=⋃_{α∈Ord}Lₐ. - Defect: L excludes measurable cardinals and large cardinals above (L⊨ "¬∃ measurable cardinal"). 3. Ultimate-L conjecture: - Goal: Construct an intra-canonical model U⊆V that accommodates all known large cardinalities. - Axiomatic requirements: U⊨GCH+strong Ω-conjecture; U compatible with super-compact/huge cardinalities; V=Ultimate-L (inevitable under Ω-logic). - Significance: If established, the continuum hypothesis (CH) can be solved and set theory unified. 5. Beyond V: Multiverse and Consistency Boundary 1. Forcing: Add "generic set G" to V through the partially ordered set ℙ to construct the expanded universe V[G]. For example, Cohen force can make V[G]⊨2^ℵ₀=ℵ₂. 2. Set theory multiverse (Multiverse): - Axiomatic framework (Hamkins): All forced expansions V[G] are equal universes. - Philosophical proposition: monism believes that V is the only absolute universe (ultimate L supporter); pluralism believes that there are infinitely many ZFC universes (force-forcing supporter). 3. Ultimate bound: - Kunen inconsistency: There is no non-trivial elementary embedding j: V→V in ZFC. - Consistency limit: Above the Berkeley cardinality, ZF axioms (such as regularity axioms) need to be sacrificed. The essence of mathematical stacking and the hierarchical pyramid (1) Consistency strength level (from low to high) Recursive ordinal (BHO) < unreachable cardinality < measurable cardinality < Woodin cardinality < ultra-compact cardinality < n-huge cardinality < Berkeley cardinality Note: The intensity of each level strictly increases, and the higher-level axioms imply the consistency of the lower-level axioms. (2) The core mechanism of stacking - recursive definition: the transition of ω→ε₀→Γ₀→BHO is achieved through ordinal functions (Veblen, OCF). - Power set axiom: drives the base expansion ℵₙ→ℵₙ₊₁, such as ℵ₀→ℵ₁→ℵ_ω. - Fixed point: satisfies κ=F(κ) (F is a hierarchical function), such as Aleph fixed point → Marlowe number. - Elementary embedding: jump from measurable cardinality to super strong cardinality through non-trivial embedding of j: V→M. - Inner model planning: construct extensions of L (e. G. L[U]→L[E→]→ultimate L) to accommodate large cardinal numbers.