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

EDITING ASSIGNMENT Find all mathematical, grammatical, stylistic, and LATEX errors in the following proof. Then rewrite it correctly on the lines below. Definition. An integer n is even iff there exists an integer k such

Source URL: users.dickinson.edu

Universit`a degli Studi di Udine Dipartimento di Matematica e Informatica Dottorato di Ricerca in Matematica e Fisica Ciclo XXVI Ph.D. Thesis

Source URL: www.math.tohoku.ac.jp

• Order theory
• Proof theory
• Mathematical logic
• Metalogic
• Equivalence of categories
• Linear extension
• Reverse mathematics
• Theorem

On weak Markov’s principle Ulrich Kohlenbach BRICS∗ Department of Computer Science University of Aarhus Ny Munkegade

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

• Constructivism
• Mathematics
• Computability theory
• Mathematical logic
• Mathematical proofs
• Functions and mappings
• Abstraction
• Proof theory
• Realizability
• Constructive proof
• Primitive recursive function
• operator

I NTRODUCTION P RINCIPLES ADMITTING A UNIVERSAL INSTANCE P RINCIPLES ADMITTING NO UNIVERSAL INSTANCE

Source URL: ludovicpatey.com

• Logic
• Computability theory
• Mathematical logic
• Proof theory
• Mathematics
• Reverse mathematics
• Model theory

PROOFS AND TYPES JEAN-YVES GIRARD Translated and with appendices by PAUL TAYLOR

Source URL: www.cs.man.ac.uk

• Logic
• Mathematical logic
• Theoretical computer science
• Proof theory
• Logic in computer science
• Models of computation
• Formal methods
• Metalogic
• Denotational semantics
• Linear logic
• Natural deduction
• Cut-elimination theorem

Math´ematiques `a rebours et un Lemme de K¨onig Faible de Type Ramsey Stage de Master 2 - MPRI mars - aoˆ ut 2012 Ludovic Patey ∗

Source URL: ludovicpatey.com

• Mathematical logic
• Computability theory
• Mathematics
• Theoretical computer science
• Proof theory
• Logic in computer science
• Theory of computation
• Second-order arithmetic
• Combinatory logic
• Reverse mathematics
• Computable function

Under consideration for publication in Math. Struct. in Comp. Science Formalization of Real Analysis: A Survey of Proof Assistants and Libraries∗ SYLVIE BOLDO CATHERINE LELAY

Source URL: www.lri.fr

• Proof assistants
• Real numbers
• Automated theorem proving
• Elementary mathematics
• Type theory
• First-order logic
• Construction of the real numbers
• Constructivism
• Mathematical logic
• Isabelle
• Axiom
• Setoid