Axiom independence
View article: Quantitative Ontology and Sole-\Chi \\From Parmenides' Axiom to Gravity and the Standard Model Structure
Quantitative Ontology and Sole-\Chi \\From Parmenides' Axiom to Gravity and the Standard Model Structure Open
This text is intended solely for academic verification, not for general public dissemination. It represents a massive blueprint evolved from a thirty-year inquiry—transforming what once seemed a coincidence into a structural necessity. We …
View article: Quantitative Ontology and Sole-\Chi \\From Parmenides' Axiom to Gravity and the Standard Model Structure
Quantitative Ontology and Sole-\Chi \\From Parmenides' Axiom to Gravity and the Standard Model Structure Open
This text is intended solely for academic verification, not for general public dissemination. It represents a massive blueprint evolved from a thirty-year inquiry—transforming what once seemed a coincidence into a structural necessity. We …
View article: The Rozum Framework: An Accountable Architecture for Emergent Cognition
The Rozum Framework: An Accountable Architecture for Emergent Cognition Open
This paper introduces the Rozum Framework (RF), a functional model that defines the minimal architecture for any accountable, self-aware, self-correcting thinking entity (rozum), regardless of physical composition. The core finding is the …
View article: Axiom Trade Invite Code "kickback" – Save 15% on Trading Fees
Axiom Trade Invite Code "kickback" – Save 15% on Trading Fees Open
Axiom Trade Invite Code “kickback”: Save 15% on Trading Fees Trading in Forex, CFDs, commodities, and cryptocurrencies can be highly rewarding, but trading fees and commissions often reduce net profits. Axiom Trade, a globally recognized b…
View article: Works for December 9, 2025 - Rule 0 - The Axiom of Foundation for Selves - John Lennon
Works for December 9, 2025 - Rule 0 - The Axiom of Foundation for Selves - John Lennon Open
Listen and ask questions here! https://notebooklm.google.com/notebook/7fc22506-5793-4a35-9052-d9d4bb3ca379
View article: Works for December 9, 2025 - Rule 0 - The Axiom of Foundation for Selves - John Lennon
Works for December 9, 2025 - Rule 0 - The Axiom of Foundation for Selves - John Lennon Open
Listen and ask questions here! https://notebooklm.google.com/notebook/7fc22506-5793-4a35-9052-d9d4bb3ca379
View article: Axiom Trade Invite Code "kickback" – Save 15% on Trading Fees
Axiom Trade Invite Code "kickback" – Save 15% on Trading Fees Open
Axiom Trade Invite Code “kickback”: Save 15% on Trading Fees Trading in Forex, CFDs, commodities, and cryptocurrencies can be highly rewarding, but trading fees and commissions often reduce net profits. Axiom Trade, a globally recognized b…
View article: The Rozum Framework: An Accountable Architecture for Emergent Cognition
The Rozum Framework: An Accountable Architecture for Emergent Cognition Open
This paper introduces the Rozum Framework (RF), a functional model that defines the minimal architecture for any accountable, self-aware, self-correcting thinking entity (rozum), regardless of physical composition. The core finding is the …
View article: The Rozum Framework: An Accountable Architecture for Emergent Cognition
The Rozum Framework: An Accountable Architecture for Emergent Cognition Open
This paper introduces the Rozum Framework (RF), a functional model that defines the minimal architecture for any accountable, self-aware, self-correcting thinking entity (rozum), regardless of physical composition. The core finding is the …
View article: Selfishness Axiom —The Essence of All Existence and Its Real-World Verification
Selfishness Axiom —The Essence of All Existence and Its Real-World Verification Open
Author's Note:This article presents a pure logical system aimed at returning to the origin and revealing the fundamental driving force behind the evolution of individuals, groups, and even civilizations. It is not a branch of any existing …
View article: Selfishness Axiom —The Essence of All Existence and Its Real-World Verification
Selfishness Axiom —The Essence of All Existence and Its Real-World Verification Open
Author's Note:This article presents a pure logical system aimed at returning to the origin and revealing the fundamental driving force behind the evolution of individuals, groups, and even civilizations. It is not a branch of any existing …
View article: A COMPARATIVE THEORETICAL ANALYSIS OF WEAK FORMS OF THE AXIOM OF CHOICE AND THEIR LOGICAL CONSEQUENCES IN ZERMELO– FRAENKEL SET THEORY
A COMPARATIVE THEORETICAL ANALYSIS OF WEAK FORMS OF THE AXIOM OF CHOICE AND THEIR LOGICAL CONSEQUENCES IN ZERMELO– FRAENKEL SET THEORY Open
This paper presents a comparative theoretical analysis of several weak forms of the Axiom of Choice (AC) andtheir logical consequences within the framework of Zermelo–Fraenkel Set Theory (ZF). While the full Axiom ofChoice ensures the exis…
View article: Independence from ZFC of an Analytic and Hypercomputational Strengthening of P=NP (and the Foundational Necessity of New Axioms for the Standard Problem
Independence from ZFC of an Analytic and Hypercomputational Strengthening of P=NP (and the Foundational Necessity of New Axioms for the Standard Problem Open
Affiliation: Private Researcher. This study presents a foundational resolution to the P versus NP problem by first establishing its independence from the standard axioms of set theory (**ZFC**). Two contradictory models are constructed: th…
View article: Independence from ZFC of an Analytic and Hypercomputational Strengthening of P=NP (and the Foundational Necessity of New Axioms for the Standard Problem
Independence from ZFC of an Analytic and Hypercomputational Strengthening of P=NP (and the Foundational Necessity of New Axioms for the Standard Problem Open
Affiliation: Private Researcher. This study presents a foundational resolution to the P versus NP problem by first establishing its independence from the standard axioms of set theory (**ZFC**). Two contradictory models are constructed: th…
View article: A COMPARATIVE THEORETICAL ANALYSIS OF WEAK FORMS OF THE AXIOM OF CHOICE AND THEIR LOGICAL CONSEQUENCES IN ZERMELO– FRAENKEL SET THEORY
A COMPARATIVE THEORETICAL ANALYSIS OF WEAK FORMS OF THE AXIOM OF CHOICE AND THEIR LOGICAL CONSEQUENCES IN ZERMELO– FRAENKEL SET THEORY Open
This paper presents a comparative theoretical analysis of several weak forms of the Axiom of Choice (AC) andtheir logical consequences within the framework of Zermelo–Fraenkel Set Theory (ZF). While the full Axiom ofChoice ensures the exis…
View article: Independence from ZFC of an Analytic and Hypercomputational Strengthening of P=NP (and the Foundational Necessity of New Axioms for the Standard Problem
Independence from ZFC of an Analytic and Hypercomputational Strengthening of P=NP (and the Foundational Necessity of New Axioms for the Standard Problem Open
Affiliation: Private Researcher. This study presents a foundational resolution to the P versus NP problem by first establishing its independence from the standard axioms of set theory (**ZFC**). Two contradictory models are constructed: th…
View article: Forcing the Continuum: Independence, Structure, and Cardinal Arithmetic Beyond CH
Forcing the Continuum: Independence, Structure, and Cardinal Arithmetic Beyond CH Open
This paper explores the profound implications of forcing techniques in set theory, focusing on the independence of the Continuum Hypothesis (CH) and the intricate structure of the continuum. We delve into the methods used to manipulate car…
View article: Forcing the Continuum: Independence, Structure, and Cardinal Arithmetic Beyond CH
Forcing the Continuum: Independence, Structure, and Cardinal Arithmetic Beyond CH Open
This paper explores the profound implications of forcing techniques in set theory, focusing on the independence of the Continuum Hypothesis (CH) and the intricate structure of the continuum. We delve into the methods used to manipulate car…
View article: Forcing the Continuum: Ordinal Scales of Cardinal Diversity
Forcing the Continuum: Ordinal Scales of Cardinal Diversity Open
This paper explores the intricate relationship between ordinal and cardinal numbers in set theory, specifically focusing on how Paul Cohen's forcing method allows for a profound manipulation of the continuum. We delve into the historical c…
View article: Forcing Architectures: Reconstructing Cardinal Arithmetic Beyond the Continuum.
Forcing Architectures: Reconstructing Cardinal Arithmetic Beyond the Continuum. Open
This paper explores the profound capabilities of forcing in set theory to reconstruct and precisely control cardinal arithmetic beyond the continuum. Building upon the foundational work of Gödel and Cohen, we investigate how various forcin…
View article: Forcing the Continuum: Ordinal Scales of Cardinal Diversity
Forcing the Continuum: Ordinal Scales of Cardinal Diversity Open
This paper explores the intricate relationship between ordinal and cardinal numbers in set theory, specifically focusing on how Paul Cohen's forcing method allows for a profound manipulation of the continuum. We delve into the historical c…
View article: Forcing Architectures: Reconstructing Cardinal Arithmetic Beyond the Continuum.
Forcing Architectures: Reconstructing Cardinal Arithmetic Beyond the Continuum. Open
This paper explores the profound capabilities of forcing in set theory to reconstruct and precisely control cardinal arithmetic beyond the continuum. Building upon the foundational work of Gödel and Cohen, we investigate how various forcin…
View article: Axiom Zero: Laws, Principles, and Rules of Structure
Axiom Zero: Laws, Principles, and Rules of Structure Open
This paper is a structural companion to the foundational Axiom Zero manuscript “Axiom Zero: Structural Irreducibility and the Unpredictability of Primes.” It assumes familiarity with the core AZ framework (survivors, cover sets, horizon wi…
View article: Beyond Naive Universes: The Axiomatic Spectrum of ZFC, NBG, and MK
Beyond Naive Universes: The Axiomatic Spectrum of ZFC, NBG, and MK Open
This paper undertakes a rigorous comparative analysis of three prominent axiomatic set theories: Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC), von Neumann-Bernays-Godel Set Theory (NBG), and Morse-Kelley Set Theory (MK). Begi…
View article: Beyond Naive Universes: The Axiomatic Spectrum of ZFC, NBG, and MK
Beyond Naive Universes: The Axiomatic Spectrum of ZFC, NBG, and MK Open
This paper undertakes a rigorous comparative analysis of three prominent axiomatic set theories: Zermelo-Fraenkel Set Theory with the Axiom of Choice (ZFC), von Neumann-Bernays-Godel Set Theory (NBG), and Morse-Kelley Set Theory (MK). Begi…
View article: Ordinal Forcing and the Cardinal Landscape of the Continuum.
Ordinal Forcing and the Cardinal Landscape of the Continuum. Open
This paper explores the profound impact of ordinal forcing techniques on shaping the cardinal landscape of the continuum within the framework of Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). We delve into the historical conte…
View article: Forcing the Continuum: Beyond Cardinal Invariants and Ordinal Definability
Forcing the Continuum: Beyond Cardinal Invariants and Ordinal Definability Open
This paper explores the intricate relationship between forcing techniques, cardinal invariants, and ordinal definability in set theory, particularly concerning the continuum. We delve into the limitations of cardinal invariants in fully ch…
View article: Forcing the Continuum: A Multiversal Perspective on Cardinal Arithmetic
Forcing the Continuum: A Multiversal Perspective on Cardinal Arithmetic Open
This paper explores the intricate landscape of cardinal arithmetic through the lens of forcing, a powerful set-theoretic technique, and interprets its implications within a multiversal perspective of set theory. We delve into the historica…
View article: The Arbitrary Continuum: Forcing the Spectrum of Cardinal Structures
The Arbitrary Continuum: Forcing the Spectrum of Cardinal Structures Open
This paper explores the profound implications of Paul Cohen's forcing technique for understanding the continuum hypothesis and, more broadly, the spectrum of cardinal structures in set theory. The continuum, the cardinality of the real num…
View article: Ordinal Forcing and the Cardinal Landscape of the Continuum.
Ordinal Forcing and the Cardinal Landscape of the Continuum. Open
This paper explores the profound impact of ordinal forcing techniques on shaping the cardinal landscape of the continuum within the framework of Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC). We delve into the historical conte…