Countable algebra and set existence axioms
From MaRDI portal
Publication:1063593
DOI10.1016/0168-0072(83)90012-XzbMath0575.03038OpenAlexW1522998756MaRDI QIDQ1063593
Rick L. Smith, Harvey M. Friedman, Stephen G. Simpson
Publication date: 1983
Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0168-0072(83)90012-x
second-order arithmeticcomprehensionencoding of structuresReverse Mathematicsweakest possible subsystem
Philosophical and critical aspects of logic and foundations (03A05) Foundations of classical theories (including reverse mathematics) (03B30) Axiomatics of classical set theory and its fragments (03E30) Second- and higher-order arithmetic and fragments (03F35)
Related Items
Ordered Groups: A Case Study in Reverse Mathematics ⋮ A rank one cohesive set ⋮ Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations? ⋮ The computability, definability, and proof theory of Artinian rings ⋮ Open Questions in Reverse Mathematics ⋮ Iterated trees and fragments of arithmetic ⋮ The role of parameters in bar rule and bar induction ⋮ A game-theoretic equivalence to the Hahn-Banach theorem ⋮ Algebraic disguises of \(\Sigma ^ 0_ 1\) induction ⋮ Herbrand analyses ⋮ Nichtbeweisbarkeit von gewissen kombinatorischen Eigenschaften endlicher Bäume;Unprovability of certain combinatorial properties of finite trees ⋮ Reverse mathematics and semisimple rings ⋮ Hilbert's program and the omega-rule ⋮ On the complexity of radicals in noncommutative rings ⋮ Degrees containing members of thin Π10 classes are dense and co-dense ⋮ Infinite versions of some problems from finite complexity theory ⋮ Stability theory and set existence axioms ⋮ The complexity of radicals and socles of modules ⋮ Degrees of orders on torsion-free abelian groups ⋮ Lifting proofs from countable to uncountable mathematics ⋮ Primitive recursive reverse mathematics ⋮ Infinite dimensional proper subspaces of computable vector spaces ⋮ Structure of semisimple rings in reverse and computable mathematics ⋮ Effective aspects of Jacobson radicals of rings ⋮ The finite intersection principle and genericity ⋮ Orders on computable rings ⋮ Reverse Mathematics of Matroids ⋮ Weak comparability of well orderings and reverse mathematics ⋮ Fixed point theory in weak second-order arithmetic ⋮ Computability-theoretic and proof-theoretic aspects of partial and linear orderings ⋮ Ring structure theorems and arithmetic comprehension ⋮ The Dirac delta function in two settings of reverse mathematics ⋮ Ideals in computable rings ⋮ Ordinal numbers and the Hilbert basis theorem ⋮ Jump degrees of torsion-free abelian groups ⋮ – CA0 and order types of countable ordered groups ⋮ Proper divisibility in computable rings ⋮ Invariants, Boolean algebras and ACA₀⁺ ⋮ The complexity of primes in computable unique factorization domains ⋮ Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation ⋮ Countable thin \(\Pi^0_1\) classes ⋮ Metric structures and probabilistic computation ⋮ Reverse mathematics and fully ordered groups ⋮ Mind change complexity of inferring unbounded unions of restricted pattern languages from positive data ⋮ Ranked structures and arithmetic transfinite recursion ⋮ Set existence axioms for general (not necessarily countable) stability theory ⋮ Connected components of graphs and reverse mathematics ⋮ Minimal prime ideals and arithmetic comprehension ⋮ On uniform relationships between combinatorial problems ⋮ Chain conditions in computable rings ⋮ The isomorphism problem for computable Abelian p-groups of bounded length ⋮ On the independence of core-equivalence results from Zermelo-Fraenkel set theory ⋮ Which set existence axioms are needed to prove the separable Hahn-Banach theorem? ⋮ European Summer Meeting of the Association for Symbolic Logic, Paris, 1985 ⋮ BOUNDS FOR INDEXES OF NILPOTENCY IN COMMUTATIVE RING THEORY: A PROOF MINING APPROACH ⋮ Characterizing von Neumann regular rings in reverse mathematics ⋮ On the ranked points of a Π10 set ⋮ Addendum to ``Countable algebra and set existence axioms ⋮ The Baire category theorem in weak subsystems of second-order arithmetic ⋮ Generalizing classical and effective model theory in theories of operations and classes ⋮ THE PREHISTORY OF THE SUBSYSTEMS OF SECOND-ORDER ARITHMETIC
Cites Work
- Skolem's solution to a problem of Frobenius
- Decidable models
- The constructive theory of countable abelian p-groups
- Effective procedures in field theory
- Effective content of field theory
- On the role of Ramsey quantifiers in first order arithmetic
- Constructions in Algebra
- Theorie Der Numerierungen III
- Computable Algebra, General Theory and Theory of Computable Fields
- Systems of predicative analysis, II: Representations of ordinals
- Decision procedures for real and p‐adic fields
- Summands of Separable Abelian Groups: Dedicated to Paul Turán on his 60th Birthday
- ∏ 0 1 Classes and Degrees of Theories
- Ramsey's theorem and recursion theory
- 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