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The continuum hypothesis
"... In this paper we prove the continuum hypothesis with categorical logic, by proving that the theory of initial ordinals and the theory of cardinals are equivalent. To prove that the theorems of the theory of cardinals are theorems of the theory of initial ordinals, and that, conversely, the theorems ..."
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In this paper we prove the continuum hypothesis with categorical logic, by proving that the theory of initial ordinals and the theory of cardinals are equivalent. To prove that the theorems of the theory of cardinals are theorems of the theory of initial ordinals, and that, conversely, the theorems
The Continuum Hypothesis
, 2011
"... The continuum hypotheses (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. In 1874 Cantor had sho ..."
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The continuum hypotheses (CH) is one of the most central open problems in set theory, one that is important for both mathematical and philosophical reasons. The problem actually arose with the birth of set theory; indeed, in many respects it stimulated the birth of set theory. In 1874 Cantor had
Justification of the Continuum Hypothesis
 COMPUTERS AND MATHEMATICS
, 1997
"... Distributing the elements of # 1 within a unit interval, intuitive arguments are given to justify the Continuum Hypothesis, suggesting that it should be accepted. ..."
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Distributing the elements of # 1 within a unit interval, intuitive arguments are given to justify the Continuum Hypothesis, suggesting that it should be accepted.
Axiomatic Derivation of the Continuum Hypothesis
 COMPUTERS AND MATHEMATICS
, 1998
"... After defining Axiom of Monotonicity, it is used along with ZermeloFraenkel set theory to derive Cantor's Continuum Hypothesis. Several related theorems are also proved. ..."
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After defining Axiom of Monotonicity, it is used along with ZermeloFraenkel set theory to derive Cantor's Continuum Hypothesis. Several related theorems are also proved.
The Independence of the General Continuum Hypothesis
"... In this paper, the independence of the generalized continuum hypothesis of the ZermeloFraenkel settheory axioms will be discussed in a manner that individuals with only a mild background in set theory can follow. This is not, however, an exhaustive trace through the details of the proof. Rather, ..."
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In this paper, the independence of the generalized continuum hypothesis of the ZermeloFraenkel settheory axioms will be discussed in a manner that individuals with only a mild background in set theory can follow. This is not, however, an exhaustive trace through the details of the proof. Rather
FORCING AXIOMS AND THE CONTINUUM HYPOTHESIS
"... One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natural to consider strengthenings of this statement in which one replaces countably ..."
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One way to formulate the Baire Category Theorem is that no compact space can be covered by countably many nowhere dense sets. Soon after Cohen’s discovery of forcing, it was realized that it was natural to consider strengthenings of this statement in which one replaces countably
headache continuum hypothesis
"... ABSTRACT Episodic paroxysmal hemicrania (EPH) is a rare disorder characterized by frequent, daily attacks of shortlived, unilateral headache with accompanying ipsilateral autonomic features. EPH has attack periods which last weeks to months separated by remission intervals lasting months to years, ..."
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the pain. Previous treatments provided no pain relief. She completely responded to indomethacin 75 mg daily. After three years, the pain recurred with longer attack duration and was just relieved with prednisone. We also propose a new hypothesis: the EPHcluster headache continuum. KEY WORDS: episodic
GENERALIZED CONTINUUM HYPOTHESIS AND THE METHOD OF FUSING
"... ABSTRACT. Method of fusing explains the basis for the formulation of the axioms of monotonicity and fusion, the two axioms which define intuitive set theory. Keywords—Continuum hypothesis, Transfinite cardinals, Infinitesimals. CONTENTS ..."
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ABSTRACT. Method of fusing explains the basis for the formulation of the axioms of monotonicity and fusion, the two axioms which define intuitive set theory. Keywords—Continuum hypothesis, Transfinite cardinals, Infinitesimals. CONTENTS
The Continuum Hypothesis, Part I
, 2001
"... Arguably the most famous formally unsolvable problem of mathematics is Hilbert’s first problem: ..."
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Arguably the most famous formally unsolvable problem of mathematics is Hilbert’s first problem:
Results 1  10
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