Michael Rathjen

Affiliations:
  • University of Leeds, Department of Pure Mathematics, UK


According to our database1, Michael Rathjen authored at least 71 papers between 1990 and 2024.

Collaborative distances:
  • Dijkstra number2 of five.
  • Erdős number3 of four.

Timeline

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Bibliography

2024
Constructing the constructible universe constructively.
Ann. Pure Appl. Log., 2024

Admissible extensions of subtheories of second order arithmetic.
Ann. Pure Appl. Log., 2024

2023
Choice and independence of premise rules in intuitionistic set theory.
Ann. Pure Appl. Log., October, 2023

2022
Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice.
Log. Methods Comput. Sci., 2022

2021
Extensional realizability for intuitionistic set theory.
J. Log. Comput., 2021

A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice.
Log. Methods Comput. Sci., 2021

No speedup for geometric theories.
CoRR, 2021

Derivatives of normal functions in reverse mathematics.
Ann. Pure Appl. Log., 2021

2020
Power Kripke-Platek set theory and the axiom of choice.
J. Log. Comput., 2020

Lifschitz Realizability as a Topological Construction.
J. Symb. Log., 2020

Minimal bad sequences are necessary for a uniform Kruskal theorem.
CoRR, 2020

2019
Preservation of choice principles under realizability.
Log. J. IGPL, 2019

Upper bounds on the graph minor theorem.
CoRR, 2019

A Note on the Ordinal Analysis of \mathbf RCA_0 + \mathrm WO(\mathbf σ ) RCA 0 + WO ( σ ).
Proceedings of the Computing with Foresight and Industry, 2019

2017
Long Sequences of Descending Theories and other Miscellanea on Slow Consistency.
FLAP, 2017

Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition.
Arch. Math. Log., 2017

An order-theoretic characterization of the Howard-Bachmann-hierarchy.
Arch. Math. Log., 2017

2016
Indefiniteness in Semi-Intuitionistic Set Theories: on a Conjecture of Feferman.
J. Symb. Log., 2016

Classifying the Provably Total set Functions of KP and KP(P).
FLAP, 2016

2015
Well-partial-orderings and the big Veblen number.
Arch. Math. Log., 2015

2014
Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience.
Ann. Pure Appl. Log., 2014

Relativized ordinal analysis: The case of Power Kripke-Platek set theory.
Ann. Pure Appl. Log., 2014

2013
Slow consistency.
Ann. Pure Appl. Log., 2013

Realizability Models Separating Various Fan Theorems.
Proceedings of the Nature of Computation. Logic, Algorithms, Applications, 2013

2012
Constructive Zermelo-Fraenkel Set Theory, Power Set, and the Calculus of Constructions.
Proceedings of the Epistemology versus Ontology, 2012

The Friedman - Sheard programme in intuitionistic logic.
J. Symb. Log., 2012

From the weak to the strong existence property.
Ann. Pure Appl. Log., 2012

Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory.
Arch. Math. Log., 2012

Ordinal Analysis and the Infinite Ramsey Theorem.
Proceedings of the How the World Computes, 2012

2010
An ordinal analysis for theories of self-referential truth.
Arch. Math. Log., 2010

A note on the theory of positive induction, ID<sup>*</sup><sub>1</sub>.
Arch. Math. Log., 2010

2009
Reverse mathematics and well-ordering principles: A pilot study.
Ann. Pure Appl. Log., 2009

2008
The natural numbers in constructive set theory.
Math. Log. Q., 2008

On the constructive Dedekind reals.
Log. Anal., 2008

2007
On the Constructive Dedekind Reals: Extended Abstract.
Proceedings of the Logical Foundations of Computer Science, International Symposium, 2007

Theories and Ordinals: Ordinal Analysis.
Proceedings of the Computation and Logic in the Real World, 2007

2006
Theories and Ordinals in Proof Theory.
Synth., 2006

A note on Bar Induction in Constructive Set Theory.
Math. Log. Q., 2006

Characterizing the interpretation of set theory in Martin-Löf typetheory.
Ann. Pure Appl. Log., 2006

Models of Intuitionistic Set Theories over Partial Combinatory Algebras.
Proceedings of the Theory and Applications of Models of Computation, 2006

2005
The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory.
Synth., 2005

Constructive Set Theory and Brouwerian Principles.
J. Univers. Comput. Sci., 2005

The disjunction and related properties for constructive Zermelo-Fraenkel set theory.
J. Symb. Log., 2005

Replacement versus collection and related topics in constructive Zermelo-Fraenkel set theory.
Ann. Pure Appl. Log., 2005

An ordinal analysis of parameter free Pi<sup>1</sup><sub>2</sub>-comprehension.
Arch. Math. Log., 2005

An ordinal analysis of stability.
Arch. Math. Log., 2005

Generalized Inductive Definitions in Constructive Set Theory.
Proceedings of the From sets and types to topology and analysis, 2005

2003
On the regular extension axiom and its variants.
Math. Log. Q., 2003

Realizing Mahlo set theory in type theory.
Arch. Math. Log., 2003

2002
Inaccessible set axions may have little consistency strength.
Ann. Pure Appl. Log., 2002

A note on the Sigma1 spectrum of a theory.
Arch. Math. Log., 2002

2001
Kripke-Platek Set Theory and the Anti-Foundation Axiom.
Math. Log. Q., 2001

The strength of Martin-Löf type theory with a superuniverse. Part II.
Arch. Math. Log., 2001

2000
The strength of Martin-Löf type theory with a superuniverse. Part I.
Arch. Math. Log., 2000

1999
Explicit Mathematics with The Monotone Fixed Point Principle. II: Models.
J. Symb. Log., 1999

1998
Explicit Mathematics with the Monotone Fixed Point Principle.
J. Symb. Log., 1998

Inaccessibility in Constructive Set Theory and Type Theory.
Ann. Pure Appl. Log., 1998

1997
On the Proof-Theoretic Strength of Monotone Induction in Explicit Mathematics.
Ann. Pure Appl. Log., 1997

1996
The Recursively Mahlo Property in Second Order Arithmetic.
Math. Log. Q., 1996

Monotone Inductive Definitions in Explicit Mathematics.
J. Symb. Log., 1996

1995
Recent advances in ordinal analysis: pi<sup>1</sup><sub>2</sub> - CA and related systems.
Bull. Symb. Log., 1995

The Higher Infinite in Proof Theory.
Proceedings of the Annual European Summer Meeting of the Association of Symbolic Logic, 1995

1994
Proof Theory of Reflection.
Ann. Pure Appl. Log., 1994

Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM.
Arch. Math. Log., 1994

The strength of some Martin-Löf type theories.
Arch. Math. Log., 1994

1993
How to Develop Proof-Theoretic Ordinal Functions on the Basis of Admissible Ordinals.
Math. Log. Q., 1993

Proof-Theoretic Investigations on Kruskal's Theorem.
Ann. Pure Appl. Log., 1993

1992
A Proof-Theoretic Characterization of the Primitive Recursive Set Functions.
J. Symb. Log., 1992

1991
The Role of Parameters in Bar Rule and Bar Induction.
J. Symb. Log., 1991

Proof-theoretic analysis of KPM.
Arch. Math. Log., 1991

1990
Ordinal notations based on a weakly Mahlo cardinal.
Arch. Math. Log., 1990


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