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Consequences of a Diagrammatic Representation of Paul Cohen’s Forcing Technique Based on C.S. Peirce’s Existential Graphs

  • Gianluca Caterina
  • Rocco Gangle
Part of the Studies in Computational Intelligence book series (SCI, volume 314)

Abstract

This article examines the forcing technique developed by Paul Cohen in his proof of the independence of the Generalized Continuum Hypothesis from the ZFC axioms of set theory in light of the theory of abductive inference and the diagrammatic system of Existential Graphs elaborated by Peirce. The history of the development of Cohen’s method is summarized, and the key steps of his technique for defining the extended model M[G] from within the ground model M are outlined. The relations between statements in M and their correspondent reference values in M[G] are modeled in Peirce’s Existential Graphs as the construction of a modal covering over the sheet of assertion. This formalization clarifies the relationship between Peirce’s EG-βand EG-γ and lays the foundation for theorizing the abductive emergence of the latter out of the former.

Keywords

Binary Sequence Diagrammatic Representation Ground Model Continuum Hypothesis Force Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gianluca Caterina
    • 1
  • Rocco Gangle
    • 1
  1. 1.Endicott CollegeBeverlyU.S.A.

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