INCOMPLETENESS VIA PARADOX AND COMPLETENESS

DOI10.1017/S1755020319000212zbMath1485.03244OpenAlexW2946546087WikidataQ127832017 ScholiaQ127832017MaRDI QIDQ5117593

Walter Dean

Publication date: 26 August 2020

Published in: The Review of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1755020319000212

zbMATH Keywords

semantic paradoxesinterpretabilityarithmetized completeness theoremDavid HilbertHilbert programPaul Bernaysset theoretic paradoxesHao WangGeorg Kreisel

Mathematics Subject Classification ID

Philosophical and critical aspects of logic and foundations (03A05) First-order arithmetic and fragments (03F30) Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62) Gödel numberings and issues of incompleteness (03F40)

Related Items

CURRENT RESEARCH ON GÖDEL’S INCOMPLETENESS THEOREMS, Reflecting and unfolding

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Liar-type paradoxes and the incompleteness phenomena
• The incompleteness theorems after 70 years
• On a paradox of Hilbert and Bernays
• Self-reference and modal logic
• Some remarks on extending and interpreting theories with a partial predicate for truth
• Sets and classes. On the work by Paul Bernays
• The theory of semisets
• Kolmogorov complexity and the second incompleteness theorem
• Hilbert's paradox
• On formalization of model-theoretic proofs of Gödel's theorems
• On interpretations of arithmetic and set theory
• Undecidable theories
• Heterologicality and Incompleteness
• On proofs of the incompleteness theorems based on Berry's paradox by Vopěnka, Chaitin, and Boolos
• Satisfying Predicates: Kleene's Proof of the Hilbert–Bernays Theorem
• Arithmetical Reflection and the Provability of Soundness
• The Surprise Examination Paradox and the Second Incompleteness Theorem
• Some applications of formalized consistency proofs
• On the paradox of grounded classes
• Arithmetization of metamathematics in a general setting
• On recursively enumerable and arithmetic models of set theory
• David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933
• David Hilbert's Lectures on the Foundations of Physics 1915-1927
• Bernays and Set Theory
• operators and alternating sentences in arithmetic
• Construction of Satisfaction Classes for Nonstandard Models
• Full Satisfaction Classes and Recursive Saturation
• Reflecting on incompleteness
• Comparison of Russell's resolution of the semantical antinomies with that of Tarski
• Relatives of the Russell Paradox
• Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I
• Yablo's paradox
• Outline of a Theory of Truth
• Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic
• TRUTH AND FEASIBLE REDUCIBILITY
• SELF-REFERENCE IN ARITHMETIC I
• SELF-REFERENCE IN ARITHMETIC II
• THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC
• Axiomatizing Kripke's theory of truth
• On Languages Which are Based on Non-Standard Arithmetic
• A survey of proof theory
• Trial and error predicates and the solution to a problem of Mostowski
• A method of modelling the formalism of set theory in axiomatic set theory
• Two notes on the foundations of set-theory
• Die schematische Korrespondenz und die idealisierten Strukturen
• The completeness of the first-order functional calculus
• A construction for consistent systems
• Some impredicative definitions in the axiomatic set theory
• Note on arithmetic models for consistent formulae of the predicate calculus
• The Hypothesis that all Classes are Nameable
• On the concepts of completeness and interpretation of formal systems
• A relative consistency proof
• A system of axiomatic set theory - Part VII
• A system of axiomatic set theory. Part III. Infinity and enumerability. Analysis
• Consistency of the Continuum Hypothesis. (AM-3)
• Recursive Predicates and Quantifiers
• Undecidable sentences generated by semantic paradoxes
• Bernays and the Completeness Theorem