| viXra.org > Set Theory and Logic > 2507 |
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| viXra.org > Set Theory and Logic > 2507 |
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[4] viXra:2507.0220 [pdf] submitted on 2025-07-31 17:30:29
Authors: Eric Louis Beaubien
Comments: 6 Pages.
The logic by and through which the universe exists can be derived directly from set theory. The fundamental principles are simple, becoming exceedingly complex in their consequences. Here, those initial principles are expounded from which a model can be rationally generated very much like the observed universe u2026 too similar to be coincidental.
Category: Set Theory and Logic
[3] viXra:2507.0149 [pdf] submitted on 2025-07-20 20:43:06
Authors: Kim Altair
Comments: 8 Pages. (Note by viXra Admin: Please cite listed scientific reference and submit article written with AI assistance to ai.viXra.org)
We examine the consequences of applying the Axiom of Choice (AC) within ZFC to the set D := R C, where C denotes the set of computable real numbers. We argue that any choice function defined on D inevitably introduces a structure in which its elements become effectively referable or indexable, thereby contradicting the definition of D as unnameable and unindexable. This leads to a logical inconsis- tency, suggesting that AC is incompatible with the existence of D. To resolve this conflict, we propose a modified axiomatic system, ZFC D/AC, in which the Axiom of Choice is explicitly restricted from applying to sets composed of non-definable real numbers. This result prompts broader meta-mathematical reflection on the in- terplay between definability, choice, and the foundational assumptions underlying mathematical existence.
Category: Set Theory and Logic
[2] viXra:2507.0148 [pdf] submitted on 2025-07-20 04:15:19
Authors: Andrey Kuznetsov
Comments: 46 Pages. Submitted to JSL on March 15, 2025
Resolution Matrix Semantics (RMS) introduces a novel truth-value-based framework for modal logic, providing a substantive alternative to Kripke’s relational semantics of possible worlds. Drawing inspiration from Y. Ivlev’s substantive semantics, RMS utilizes a 4-valued structure—necessary truth (tn), contingent truth (tc), contingent false (fc), and necessary false (fn)—augmented by indeterminate values (t, f, t/f) to define modal systems Km, KDm, KTm, S4m, and S5m, analogous to Kripke’s K, KD, T, S4, and S5. By directly assigning determined and indeterminate truth values via an interpretation function, RMS validates formulas without relying on accessibility relations, as demonstrated through soundness and completeness proofs and a tailored tableau method. The framework’s versatility extends to applications in deontic logic, artificial intelligence, and quantum computing, enabling context-dependent reasoning with computational efficiency. RMS thus bridges philosophical logic and practical domains, offering a truth-centric perspective on modal reasoning’s complexities.
Category: Set Theory and Logic
[1] viXra:2507.0045 [pdf] submitted on 2025-07-06 01:24:18
Authors: Eric Louis Beaubien
Comments: 2 Pages. (Note by viXra Admin: Please cite and list scientific references)
Symmetry violations like parity non-conservation and the absence of antimatter may have a simple explanation requiring very little analysis. We need only accept that the universe is a ‘logical’ construct that includes the observer as an integral part. Our subjective observations are duly accounted for by that logic.
Category: Set Theory and Logic
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