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\(\mathrm {ZF}\) Between Classicality and Non-classicality

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Abstract

We present a generalization of the algebra-valued models of \(\mathrm {ZF}\) where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \(\mathrm {ZF}\).

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Acknowledgements

The first author wants to acknowledge FAPESP for providing the Visiting Researcher grant n. 2019/12527-0 in the University of Campinas, Brazil for one year and this research work is done during this period. The second author acknowledge the generous support of FAPESP through the Jovem Pesquisador grant n. 2016/25891-3.

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Authors and Affiliations

  1. St. Xavier’s College, 30 Mother Teresa Sarani, Kolkata, West Bengal, 700016, India

    Sourav Tarafder

  2. University of Campinas (UNICAMP), IFCH, Barão Geraldo, SP, 13083-896, Brazil

    Sourav Tarafder & Giorgio Venturi

Authors
  1. Sourav Tarafder
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  2. Giorgio Venturi
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Correspondence to Giorgio Venturi.

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Tarafder, S., Venturi, G. \(\mathrm {ZF}\) Between Classicality and Non-classicality. Stud Logica 110, 189–218 (2022). https://doi.org/10.1007/s11225-021-09959-w

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  • DOI: https://doi.org/10.1007/s11225-021-09959-w

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