Forcing the Continuum: Independence, Structure, and Cardinal Arithmetic Beyond CH Article Swipe
Revista, Zen
,
MATH, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17839825
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17839825
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 cardinal arithmetic, particularly beyond the assumption of CH, examining how forcing allows us to construct models of set theory where the continuum has various cardinalities and exhibits diverse structural properties. The paper provides a comprehensive overview of key forcing constructions, including Cohen forcing, iterated forcing, and forcing with large cardinals, to establish independence results concerning the continuum. Furthermore, we investigate the consequences of these independence results on other areas of mathematics, such as real analysis, topology, and measure theory. The goal is to offer a detailed exposition of the current state of knowledge regarding the continuum and its intricate relationship with the axioms of set theory.
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All OpenAlex metadata
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https://doi.org/10.5281/zenodo.17839825Digital Object Identifier
- Title
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Forcing the Continuum: Independence, Structure, and Cardinal Arithmetic Beyond CHWork title
- Type
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articleOpenAlex work type
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2025Year of publication
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2025-12-06Full publication date if available
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Revista, Zen, MATH, 10List of authors in order
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https://doi.org/10.5281/zenodo.17839825Publisher landing page
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://doi.org/10.5281/zenodo.17839825Direct OA link when available
- Concepts
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Forcing (mathematics), Axiom, Mathematics, Iterated function, Independence (probability theory), Set (abstract data type), Set theory, Exposition (narrative), Construct (python library), Mathematical economics, Sketch, Discrete mathematics, Calculus (dental), Measure (data warehouse), Axiom independenceTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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