Classes and truths in set theory

DOI10.1016/j.apal.2011.12.006zbMath1300.03010OpenAlexW2052199430MaRDI QIDQ450946

Kentaro Fujimoto

Publication date: 26 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.apal.2011.12.006

zbMATH Keywords

proof theoryset theorytheory of truthclass theoryglobal choice.

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) Nonclassical and second-order set theories (03E70) Proof theory in general (including proof-theoretic semantics) (03F03)

Related Items (23)

One hundred years of semantic paradox ⋮ THE COPERNICAN MULTIVERSE OF SETS ⋮ Set theoretical analogues of the Barwise-Schlipf theorem ⋮ A fixed point theory over stratified truth ⋮ First‐order undefinability of the notion of transfinitely uplifting cardinals ⋮ Open determinacy for class games ⋮ Inner mantles and iterated HOD ⋮ VARIETIES OF CLASS-THEORETIC POTENTIALISM ⋮ A few more dissimilarities between second-order arithmetic and set theory ⋮ Disquotation and infinite conjunctions ⋮ Full and hat inductive definitions are equivalent in NBG ⋮ Set-theoretic blockchains ⋮ TRUTHS, INDUCTIVE DEFINITIONS, AND KRIPKE-PLATEK SYSTEMS OVER SET THEORY ⋮ Elementary inductive dichotomy: separation of open and clopen determinacies with infinite alternatives ⋮ Feferman and the Truth ⋮ MODAL STRUCTURALISM AND REFLECTION ⋮ Deflationism beyond arithmetic ⋮ MINIMUM MODELS OF SECOND-ORDER SET THEORIES ⋮ UNIVERSISM AND EXTENSIONS OF V ⋮ THE EXACT STRENGTH OF THE CLASS FORCING THEOREM ⋮ THE EXPRESSIVE POWER OF TRUTH ⋮ FINITIST AXIOMATIC TRUTH ⋮ A note on typed truth and consistency assertions

Cites Work

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• On Feferman's operational set theory \textsf{OST}
• RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES
• Relative Truth Definability of Axiomatic Truth Theories
• Autonomous progression and transfinite iteration of self-applicable truth
• A theory of formal truth arithmetically equivalent to ID₁
• AXIOMS FOR DETERMINATENESS AND TRUTH
• Notes on Formal Theories of Truth
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• Comparison of the axioms of local and universal choice
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• Transfinite recursive progressions of axiomatic theories
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