A MODEL OF SECOND-ORDER ARITHMETIC SATISFYING AC BUT NOT DC SY-DAVID FRIEDMAN AND VICTORIA GITMAN Abstract. We show that there is a β-model of second-order arithmetic in which the choice scheme holds, but the dependent

Source URL: victoriagitman.github.io

Introduction Descriptive Set Theory in SOA Collapsing a model of ZFC Sharps # Collapsing a model of ZFC

Source URL: www.math.uni-bonn.de

• Mathematics
• Mathematical logic
• Logic
• Foundations of mathematics
• Z notation
• ZermeloFraenkel set theory
• Determinacy
• Set theory
• Second-order arithmetic
• Constructible universe
• Model theory
• Descriptive set theory

TERM EXTRACTION AND RAMSEY’S THEOREM FOR PAIRS ALEXANDER P. KREUZER AND ULRICH KOHLENBACH Abstract. In this paper we study with proof-theoretic methods the function(al)s provably recursive relative to Ramsey’s theore

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

• Proof theory
• Computability theory
• Logic in computer science
• Mathematical logic
• Intuitionism
• Primitive recursive functional
• Dialectica interpretation
• Peano axioms
• Second-order arithmetic
• Reverse mathematics
• Combinatory logic
• Primitive recursive arithmetic

BROWN’S LEMMA IN SECOND-ORDER ARITHMETIC EMANUELE FRITTAION Abstract. We show that Brown’s lemma is equivalent to IΣ02 over RCA∗0 . We also show that (the infinite) van der Waerden’s theorem is equivalent to BΣ

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

• Mathematics
• Ergodic theory
• Ramsey theory
• Semigroup theory
• Lemmas
• Combinatorics
• Piecewise syndetic set
• Partition regularity
• Syndetic set
• Diagonal lemma
• IP set
• BanachAlaoglu theorem

Investigations of Subsystems of Second Order Arithmetic and Set Theory in Strength between Π11 -CA and ∆12 -CA + BI: Part I Michael Rathjen Department of Pure Mathematics University of Leeds

Source URL: www1.maths.leeds.ac.uk

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

Introduction Results Maximal chains in second-order arithmetic Emanuele Frittaion

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

• Mathematics
• Algebra
• Geometry
• Wellfoundedness
• Ordinal number
• Constructible universe
• Convex cone
• Height
• Hlder condition
• Axiom of limitation of size

Formalizing forcing arguments in subsystems of second-order arithmetic Ulrik Buchholtz Stanford April 26, 2011

Source URL: www.andrew.cmu.edu

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

THE WEAKNESS OF BEING COHESIVE, THIN OR FREE IN REVERSE MATHEMATICS LUDOVIC PATEY Abstract. Informally, a mathematical statement is robust if its strength is left unchanged under variations of the statement. In this pape

Source URL: ludovicpatey.com

• Computability theory
• Computable function
• Computation in the limit
• Second-order arithmetic
• Compactness theorem
• Reverse mathematics
• 01 class
• PA degree
• Low
• Algorithmically random sequence
• Computable number