The axiom of choice

DOI10.1016/0022-4049(80)90097-3zbMath0446.03042OpenAlexW1996947986WikidataQ114685099 ScholiaQ114685099MaRDI QIDQ5904544

Peter J. Freyd

Publication date: 1980

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(80)90097-3

zbMATH Keywords

topos of sheavesaxiom of choiceGrothendieck toposmonoid representationsexponential varietyinterpretation of ZF in the topos of double-negation sheaveswell-foundedness of the topos of double-negation sheaveswell-ordered families

Mathematics Subject Classification ID

Categorical logic, topoi (03G30) Topoi (18B25) Consistency and independence results (03E35) Nonclassical and second-order set theories (03E70) Factorization systems, substructures, quotient structures, congruences, amalgams (18A32) Axiom of choice and related propositions (03E25) Other aspects of forcing and Boolean-valued models (03E40)

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Nominal logic, a first order theory of names and binding ⋮ Non-well-founded trees in categories ⋮ What do Freyd's toposes classify? ⋮ Sheaf models for set theory ⋮ Unnamed Item ⋮ The World's simplest axiom of choice fails ⋮ Introduction: A personal tribute to Peter Freyd and Bill Lawvere ⋮ The associated sheaf functor theorem in algebraic set theory ⋮ Aspects of predicative algebraic set theory. I: Exact completion ⋮ Cohen and Set Theory ⋮ Lawvere–Tierney sheaves in Algebraic Set Theory ⋮ Quotients of decidable objects in a topos ⋮ Abelian groups in a topos: injectives and injective effacements

Cites Work

• Sheaf models for set theory
• Aspects of topoi