Forcing the Continuum: A Multiversal Perspective on Cardinal Arithmetic Article Swipe
Revista, Zen
,
MATH, 10
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17832935
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.5281/zenodo.17832935
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 historical context of the Continuum Hypothesis (CH) and its generalized form (GCH), highlighting their independence from the Zermelo-Fraenkel axioms with the Axiom of Choice (ZFC). The methodology section rigorously details the forcing technique, explaining how it enables the construction of diverse models of ZFC where cardinal arithmetic statements, particularly those concerning the continuum, can take on various consistent values. Results demonstrate specific forcing constructions that make CH true or false, and allow the continuum to be any regular cardinal greater than $aleph_1$. The discussion contextualizes these findings within the emerging concept of a set-theoretic multiverse, arguing that such a perspective offers a coherent framework for understanding the profound independence results and the inherent plurality of mathematical universes. We conclude that forcing is not merely a tool for consistency proofs, but a fundamental method for mapping the boundaries and internal structures of this rich multiversal reality, profoundly shaping our understanding of infinitary mathematics.
Related Topics
Concepts
Forcing (mathematics)
Axiom
Mathematics
Perspective (graphical)
Consistency (knowledge bases)
Independence (probability theory)
Context (archaeology)
Axiom independence
Calculus (dental)
Mathematical logic
Mathematical economics
Epistemology
Set (abstract data type)
Algebra over a field
Set theory
Section (typography)
Absoluteness
Metadata
- Type
- article
- Landing Page
- https://doi.org/10.5281/zenodo.17832935
- OA Status
- green
- OpenAlex ID
- https://openalex.org/W7109115535
All OpenAlex metadata
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https://openalex.org/W7109115535Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.5281/zenodo.17832935Digital Object Identifier
- Title
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Forcing the Continuum: A Multiversal Perspective on Cardinal ArithmeticWork title
- Type
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articleOpenAlex work type
- Publication year
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2025Year of publication
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2025-12-05Full 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.17832935Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://doi.org/10.5281/zenodo.17832935Direct OA link when available
- Concepts
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Forcing (mathematics), Axiom, Mathematics, Perspective (graphical), Consistency (knowledge bases), Independence (probability theory), Context (archaeology), Axiom independence, Calculus (dental), Mathematical logic, Mathematical economics, Epistemology, Set (abstract data type), Algebra over a field, Set theory, Section (typography), AbsolutenessTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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