Logical metatheorems for abstract spaces axiomatized in positive bounded logic

DOI10.1016/j.aim.2015.12.007zbMath1402.03078OpenAlexW2182766684MaRDI QIDQ908073

Ulrich Kohlenbach, Daniel Günzel

Publication date: 2 February 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2015.12.007

zbMATH Keywords

uniform boundedness principleultrapowerproof miningpositive bounded logic

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Banach lattices (46B42) Ultraproduct techniques in Banach space theory (46B08) Functionals in proof theory (03F10) Ultraproducts and related constructions (03C20)

Related Items (7)

A proof-theoretic bound extraction theorem for \(\mathrm{CAT}(\kappa)\)-spaces ⋮ A uniform betweenness property in metric spaces and its role in the quantitative analysis of the ``lion-man game ⋮ A proof‐theoretic metatheorem for tracial von Neumann algebras ⋮ Quantitative results on Fejér monotone sequences ⋮ The finitary content of sunny nonexpansive retractions ⋮ Rates of convergence and metastability for abstract Cauchy problems generated by accretive operators ⋮ PROOF MINING IN L^p SPACES

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rates of convergence and metastability for abstract Cauchy problems generated by accretive operators
• Nonsquareness and locally uniform nonsquareness in Orlicz-Bochner function spaces endowed with Luxemburg norm
• Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation
• Effective metastability of Halpern iterates in \(CAT(0)\) spaces
• Pointwise hereditary majorization and some applications
• On the theory of \(L_p (L_q)\)-Banach lattices
• Nonstandard methods in fixed point theory
• Banach lattices
• On \(P\)- and \(p\)-convexity of Banach spaces
• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• Uniformly non-square Banach spaces
• Ultraproducts and metastability
• Quantitative image recovery theorems
• Bounded functional interpretation
• Measures defined by abstract \(L_{p}\) spaces
• The asymptotic behavior of the solutions of the Cauchy problem generated by \(\phi\)-accretive operators
• Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.)
• Ultrafilters in reverse mathematics
• NON-PRINCIPAL ULTRAFILTERS, PROGRAM EXTRACTION AND HIGHER-ORDER REVERSE MATHEMATICS
• On the computational content of convergence proofs via Banach limits
• Metastability in the Furstenberg–Zimmer tower
• A metastable dominated convergence theorem
• Strongly majorizable functionals of finite type: A model for barrecursion containing discontinuous functionals
• Some logical metatheorems with applications in functional analysis
• A Logical Uniform Boundedness Principle for Abstract Metric and Hyperbolic Spaces
• CONTINUOUS FIRST ORDER LOGIC FOR UNBOUNDED METRIC STRUCTURES
• General logical metatheorems for functional analysis
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
• Continuous Model Theory. (AM-58)
• Absolutely summing operators in $ℒ_{p}$-spaces and their applications
• Packing and Reflexivity in Banach Spaces
• Über die Charakterisierung des allgemeinen $C$-Raumes

This page was built for publication: Logical metatheorems for abstract spaces axiomatized in positive bounded logic