Arithmetization of metamathematics in a general setting
From MaRDI portal
Publication:3273298
DOI10.4064/fm-49-1-35-92zbMath0095.24301OpenAlexW1571003765MaRDI QIDQ3273298
Publication date: 1960
Published in: Fundamenta Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/213578
Related Items
Deduction-preserving “recursive isomorphisms” between theories, Logische Kategorien, SELF-REFERENCE UPFRONT: A STUDY OF SELF-REFERENTIAL GÖDEL NUMBERINGS, Finitely axiomatized theories lack self‐comprehension, AN ESCAPE FROM VARDANYAN’S THEOREM, A step towards absolute versions of metamathematical results, Bicontextualism, Varieties of self-reference in metamathematics, 1 — Consistency and faithful interpretations, A NOTE ON DERIVABILITY CONDITIONS, Reflection algebras and conservation results for theories of iterated truth, VARIANTS OF KREISEL’S CONJECTURE ON A NEW NOTION OF PROVABILITY, On bimodal logics of provability, Proof Theory in Philosophy of Mathematics, An Arithmetical Interpretation of Verification and Intuitionistic Knowledge, Unwinding modal paradoxes on digraphs, A NOTE ON FRAGMENTS OF UNIFORM REFLECTION IN SECOND ORDER ARITHMETIC, A simple dynamic logic, Franco Montagna's work on provability logic and many-valued logic, Interpretability of various extensions of arithmetic, On formalization of model-theoretic proofs of Gödel's theorems, A Fortuitous Year with Leon Henkin, The Henkin Sentence, Kripke Models Built from Models of Arithmetic, Lindenbaum Algebras and Partial Conservativity, Designing paradoxes: a revision-theoretic approach, Friedman-reflexivity, Inconsistency of a metatheory of Nudel'man, Hard provability logics, Interpretability suprema in Peano arithmetic, The incompleteness theorems after 70 years, The absorption law. Or: how to Kreisel a Hilbert-Bernays-Löb, Short proofs for slow consistency, On predicate provability logics and binumerations of fragments of Peano arithmetic, Passive induction and a solution to a Paris-Wilkie open question, Informal versus formal mathematics, Positive provability logic for uniform reflection principles, Petr Hájek: A Scientific Biography, Rosser provability and normal modal logics, Henkin sentences and local reflection principles for Rosser provability, ANOTHER LOOK AT THE SECOND INCOMPLETENESS THEOREM, RELEVANCE FOR THE CLASSICAL LOGICIAN, Computability of partial functions and enumerability of sets in Peano's arithmetic, GENERALIZATIONS OF GÖDEL’S INCOMPLETENESS THEOREMS FOR ∑n-DEFINABLE THEORIES OF ARITHMETIC, IN MEMORIAM: SOLOMON FEFERMAN (1928–2016), Transductions in arithmetic, The fixed point property in modal logic, Interpretations of the first-order theory of diagonalizable algebras in Peano arithmetic, INCOMPLETENESS VIA PARADOX AND COMPLETENESS, The logical strength of compositional principles, Consequences of an exotic definition for \(\text{P}=\text{NP}\)., Binumerability in a sequence of theories, Reflection calculus and conservativity spectra, The second incompleteness theorem and bounded interpretations, Arithmetic, set theory, reduction and explanation, Montague's paradox, informal provability, and explicit modal logic, The formalization of interpretability, Predicate provability logic with non-modalized quantifiers, More on Systems of Truth and Predicative Comprehension, The de Jongh property for basic arithmetic, Yablifying the Rosser sentence, Rosser-type undecidable sentences based on Yablo's paradox, Proof Theoretic Analysis by Iterated Reflection, Arithmetical completeness theorem for modal logic \(\mathsf{K}\), Peano Corto and Peano Basso: A Study of Local Induction in the Context of Weak Theories, Conventionalism, consistency, and consistency sentences, A generalized notion of weak interpretability and the corresponding modal logic, On \(\Sigma _ 1\) and \(\Pi _ 1\) sentences and degrees of interpretability, On partial disjunction properties of theories containing Peano arithmetic, Arithmetical soundness and completeness for \(\Sigma_{2}\) numerations, The Axiom System IΣ0 Manages to Simultaneously Obey and Evade the Herbrandized Version of the Second Incompleteness Theorem, Independent numerations of theories and recursive progressions, Problemi aperti sulle algebre diagonali, Uniform density in Lindenbaum algebras, Fixed point algebras, Structuralism and meta-mathematics, Significato e verita nell'aritmetica peaniana, Experimental logics and \(\Delta^0_2\)-theories, Relativity phenomena in set theory, Un'estensione del teorema di Lob, The predicative Frege hierarchy, On expandability of models of Peano arithmetic. I, The \(\Sigma_1\)-provability logic of \(\mathsf{HA}\), On expandability of models of Peano arithmetic. III, PROVABILITY LOGICS RELATIVE TO A FIXED EXTENSION OF PEANO ARITHMETIC, Some specially formulated axiomizations for \(\mathrm{I}\Sigma _0\) manage to evade the Herbrandized version of the second incompleteness theorem, The neglect of epistemic considerations in logic: the case of epistemic assumptions, Partially Conservative Extensions of Arithmetic, CURRENT RESEARCH ON GÖDEL’S INCOMPLETENESS THEOREMS, On the algebraization of a Feferman's predicate. (The algebraization of theories which express Theor; X), Arithmetical hierarchy and complexity of computation, On the set of 'meaningful' sentences of arithmetic, The Interpretation Existence Lemma, A sequence of theories for arithmetic whose union is complete, The implicit commitment of arithmetical theories and its semantic core, Intensionality in mathematics, Tarski on ``essentially richer metalanguages, Conservativity spectra and Joosten-Fernández model, The closed fragment of the interpretability logic of PRA with a constant for I\(\Sigma^1\), ON THE INVARIANCE OF GÖDEL’S SECOND THEOREM WITH REGARD TO NUMBERINGS, Predicate logics of expressively strong theories, Su certe teorie non enumerabili. (Sulle limitazioni dei sistemi formali. I.), Some problems of completeness of arithmetic, Rosser provability and the second incompleteness theorem, The arithmetics of a theory, Some independence results in interpretability logic, HIERARCHICAL INCOMPLETENESS RESULTS FOR ARITHMETICALLY DEFINABLE EXTENSIONS OF FRAGMENTS OF ARITHMETIC, EQUIVALENCES FOR TRUTH PREDICATES, There is no plus-capping degree, A note on typed truth and consistency assertions
