THE ADDITIVITY OF TRACES IN MONOIDAL DERIVATORS MORITZ GROTH, KATE PONTO AND MICHAEL SHULMAN Abstract. We develop the theory of monoidal structures on derivators, culminating in a proof that generalized trace maps in a c

Source URL: www.math.ru.nl

Real Growth in Standard Parts of Analysis∗ Ulrich Kohlenbach Fachbereich Mathematik J.W. Goethe Universit¨at Robert-Mayer-StrFrankfurt am Main, Germany

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Functions and mappings
• Recursion
• Theory of computation
• Proof theory
• Primitive recursive function
• Continuous function
• Elementary function arithmetic
• Arithmetic function

Applied Foundations: Proof Mining in Mathematics Ulrich Kohlenbach BRICS∗ Department of Computer Science University of Aarhus Ny Munkegade

Source URL: www.mathematik.tu-darmstadt.de

• Logic
• Proof theory
• Mathematical logic
• Mathematics
• Proof mining
• Mathematical proof
• Consistency
• Constructive proof
• Formal proof
• Intuitionistic logic
• Approximation
• Type theory

Proof Interpretations with Truth∗ Jaime Gaspar† Paulo Oliva‡ 12 August 2009

Source URL: jg.sdf.org

• Logic
• Constructivism
• Mathematical logic
• Proof theory
• Abstraction
• Predicate logic
• Dependently typed programming
• Intuitionism
• Realizability
• BrouwerHeytingKolmogorov interpretation
• Intuitionistic logic
• Quantifier

Problem statement Undecidability Decidability

Source URL: a3nm.net

• Logic
• Computing
• Proof theory
• Philosophy
• Decidability
• Metalogic
• Artificial intelligence
• Non-classical logic
• Conjunctive query
• Description logic
• Web Ontology Language

On the Computational Content of the Bolzano-Weierstraß Principle∗ Pavol Safarik and Ulrich Kohlenbach Department of Mathematics Technische Universität Darmstadt Schlossgartenstraße 7, 64289 Darmstadt, Germany

Source URL: www.mathematik.tu-darmstadt.de

• Proof theory
• Logic
• Mathematical logic
• Mathematics
• Computability theory
• Primitive recursive functional
• Dialectica interpretation
• Combinatory logic
• Continuous function

Equihash: Asymmetric Proof-of-Work Based on the Generalized Birthday Problem Alex Biryukov Dmitry Khovratovich

Source URL: www.internetsociety.org

• Computational complexity theory
• Theory of computation
• Complexity classes
• Analysis of algorithms
• Finite fields
• NP
• Spacetime tradeoff
• Algorithm
• Time complexity
• IP
• P
• XTR

Extending Superposition with Integer Arithmetic, Structural Induction, and Beyond Simon Cruanes École polytechnique and Inria https://who.rocq.inria.fr/Simon.Cruanes/

Source URL: cedeela.fr

• Mathematical logic
• Theoretical computer science
• Mathematics
• Automated theorem proving
• Logic in computer science
• Model theory
• First-order logic
• Mathematical proof
• Unification
• Equality

Herbrand’s theorem and extractive proof theory U. Kohlenbach Department of Mathematics Technische Universit¨at Darmstadt Schlossgartenstrasse 7, 64289 Darmstadt, Germany September 1, 2008

Source URL: www.mathematik.tu-darmstadt.de

• Mathematics
• Mathematical analysis
• Mathematical logic
• Functions and mappings
• Computability theory
• Primitive recursive function
• Recursion
• Theory of computation
• First-order logic
• Limit of a function
• Peano axioms
• Spectral theory of ordinary differential equations

FOUNDATIONAL AND MATHEMATICAL USES OF HIGHER TYPES ULRICH KOHLENBACH† DEDICATED TO SOLOMON FEFERMAN FOR HIS 70TH BIRTHDAY §1. Introduction. A central theme of proof theory is expressed by the following question:

Source URL: www.mathematik.tu-darmstadt.de

• Computability theory
• Proof theory
• Mathematical logic
• Metalogic
• Reverse mathematics
• Primitive recursive functional
• Second-order arithmetic
• Peano axioms
• Primitive recursive function
• Primitive recursive arithmetic
• Model theory
• Symbol