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ORCIDMichael Rathjen
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- affiliation: University of Leeds, Department of Pure Mathematics, UK
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Journal Articles
- 2024
[j59]Richard Matthews, Michael Rathjen:
Constructing the constructible universe constructively. Ann. Pure Appl. Log. 175(3): 103392 (2024)- [j58]Gerhard Jäger
, Michael Rathjen:
Admissible extensions of subtheories of second order arithmetic. Ann. Pure Appl. Log. 175(7): 103425 (2024) - 2023
- [j57]Emanuele Frittaion, Takako Nemoto, Michael Rathjen:
Choice and independence of premise rules in intuitionistic set theory. Ann. Pure Appl. Log. 174(9): 103314 (2023) - 2022
- [j56]Maria Emilia Maietti, Samuele Maschio, Michael Rathjen:
Inductive and Coinductive Topological Generation with Church's thesis and the Axiom of Choice. Log. Methods Comput. Sci. 18(4) (2022) - 2021
- [j55]Anton Freund, Michael Rathjen:
Derivatives of normal functions in reverse mathematics. Ann. Pure Appl. Log. 172(2): 102890 (2021) - [j54]Maria Emilia Maietti, Samuele Maschio, Michael Rathjen:
A realizability semantics for inductive formal topologies, Church's Thesis and Axiom of Choice. Log. Methods Comput. Sci. 17(2) (2021) - [j53]Emanuele Frittaion, Michael Rathjen:
Extensional realizability for intuitionistic set theory. J. Log. Comput. 31(2): 630-653 (2021) - 2020
- [j52]Michael Rathjen, Andrew W. Swan:
Lifschitz Realizability as a Topological Construction. J. Symb. Log. 85(4): 1342-1375 (2020) - [j51]Michael Rathjen:
Power Kripke-Platek set theory and the axiom of choice. J. Log. Comput. 30(1): 447-457 (2020) - 2019
- [j50]Eman Dihoum, Michael Rathjen:
Preservation of choice principles under realizability. Log. J. IGPL 27(5): 746-765 (2019) - 2017
- [j49]Jeroen Van der Meeren, Michael Rathjen, Andreas Weiermann:
An order-theoretic characterization of the Howard-Bachmann-hierarchy. Arch. Math. Log. 56(1-2): 79-118 (2017) - [j48]Michael Rathjen, Jeroen Van der Meeren, Andreas Weiermann:
Ordinal notation systems corresponding to Friedman's linearized well-partial-orders with gap-condition. Arch. Math. Log. 56(5-6): 607-638 (2017) - [j47]Michael Rathjen:
Long Sequences of Descending Theories and other Miscellanea on Slow Consistency. FLAP 4(4) (2017) - 2016
- [j46]Michael Rathjen, Jacob Cook:
Classifying the Provably Total set Functions of KP and KP(P). FLAP 3(4): 681-753 (2016) - [j45]Michael Rathjen:
Indefiniteness in Semi-Intuitionistic Set Theories: on a Conjecture of Feferman. J. Symb. Log. 81(2): 742-754 (2016) - 2015
- [j44]Jeroen Van der Meeren, Michael Rathjen, Andreas Weiermann:
Well-partial-orderings and the big Veblen number. Arch. Math. Log. 54(1-2): 193-230 (2015) - 2014
- [j43]Michael Rathjen:
Relativized ordinal analysis: The case of Power Kripke-Platek set theory. Ann. Pure Appl. Log. 165(1): 316-339 (2014) - [j42]Michael Rathjen:
Constructive Zermelo-Fraenkel set theory and the limited principle of omniscience. Ann. Pure Appl. Log. 165(2): 563-572 (2014) - 2013
- [j41]Sy-David Friedman, Michael Rathjen, Andreas Weiermann:
Slow consistency. Ann. Pure Appl. Log. 164(3): 382-393 (2013) - 2012
- [j40]Ray-Ming Chen, Michael Rathjen:
Lifschitz realizability for intuitionistic Zermelo-Fraenkel set theory. Arch. Math. Log. 51(7-8): 789-818 (2012) - [j39]Michael Rathjen:
From the weak to the strong existence property. Ann. Pure Appl. Log. 163(10): 1400-1418 (2012) - [j38]Graham Emil Leigh, Michael Rathjen:
The Friedman - Sheard programme in intuitionistic logic. J. Symb. Log. 77(3): 777-806 (2012) - 2010
- [j37]Graham Emil Leigh, Michael Rathjen:
An ordinal analysis for theories of self-referential truth. Arch. Math. Log. 49(2): 213-247 (2010) - [j36]Bahareh Afshari, Michael Rathjen:
A note on the theory of positive induction, ID*1. Arch. Math. Log. 49(2): 275-281 (2010) - 2009
- [j35]Bahareh Afshari, Michael Rathjen:
Reverse mathematics and well-ordering principles: A pilot study. Ann. Pure Appl. Log. 160(3): 231-237 (2009) - 2008
- [j34]Robert S. Lubarsky, Michael Rathjen:
On the constructive Dedekind reals. Log. Anal. 1(2): 131-152 (2008) - [j33]Michael Rathjen:
The natural numbers in constructive set theory. Math. Log. Q. 54(1): 83-97 (2008) - 2006
- [j32]Michael Rathjen, Sergei Tupailo:
Characterizing the interpretation of set theory in Martin-Löf typetheory. Ann. Pure Appl. Log. 141(3): 442-471 (2006) - [j31]Michael Rathjen:
A note on Bar Induction in Constructive Set Theory. Math. Log. Q. 52(3): 253-258 (2006) - [j30]Michael Rathjen:
Theories and Ordinals in Proof Theory. Synth. 148(3): 719-743 (2006) - 2005
- [j29]Michael Rathjen:
An ordinal analysis of stability. Arch. Math. Log. 44(1): 1-62 (2005) - [j28]Michael Rathjen:
An ordinal analysis of parameter free Pi12-comprehension. Arch. Math. Log. 44(3): 263-362 (2005) - [j27]Michael Rathjen:
Replacement versus collection and related topics in constructive Zermelo-Fraenkel set theory. Ann. Pure Appl. Log. 136(1-2): 156-174 (2005) - [j26]Michael Rathjen:
The disjunction and related properties for constructive Zermelo-Fraenkel set theory. J. Symb. Log. 70(4): 1233-1254 (2005) - [j25]Michael Rathjen:
Constructive Set Theory and Brouwerian Principles. J. Univers. Comput. Sci. 11(12): 2008-2033 (2005) - [j24]Michael Rathjen:
The Constructive Hilbert Program and the Limits of Martin-Löf Type Theory. Synth. 147(1): 81-120 (2005) - 2003
- [j23]Michael Rathjen:
Realizing Mahlo set theory in type theory. Arch. Math. Log. 42(1): 89-101 (2003) - [j22]Michael Rathjen, Robert S. Lubarsky:
On the regular extension axiom and its variants. Math. Log. Q. 49(5): 511-518 (2003) - 2002
- [j21]Michael Möllerfeld, Michael Rathjen:
A note on the Sigma1 spectrum of a theory. Arch. Math. Log. 41(1): 33-34 (2002) - [j20]Laura Crosilla, Michael Rathjen:
Inaccessible set axions may have little consistency strength. Ann. Pure Appl. Log. 115(1-3): 33-70 (2002) - 2001
- [j19]Michael Rathjen:
The strength of Martin-Löf type theory with a superuniverse. Part II. Arch. Math. Log. 40(3): 207-233 (2001) - [j18]Michael Rathjen:
Kripke-Platek Set Theory and the Anti-Foundation Axiom. Math. Log. Q. 47(4): 435-440 (2001) - 2000
- [j17]Michael Rathjen:
The strength of Martin-Löf type theory with a superuniverse. Part I. Arch. Math. Log. 39(1): 1-39 (2000) - 1999
- [j16]Michael Rathjen:
Explicit Mathematics with The Monotone Fixed Point Principle. II: Models. J. Symb. Log. 64(2): 517-550 (1999) - 1998
- [j15]Michael Rathjen, Edward R. Griffor, Erik Palmgren:
Inaccessibility in Constructive Set Theory and Type Theory. Ann. Pure Appl. Log. 94(1-3): 181-200 (1998) - [j14]Michael Rathjen:
Explicit Mathematics with the Monotone Fixed Point Principle. J. Symb. Log. 63(2): 509-542 (1998) - 1997
- [j13]Thomas Glaß, Michael Rathjen, Andreas Schlüter:
On the Proof-Theoretic Strength of Monotone Induction in Explicit Mathematics. Ann. Pure Appl. Log. 85(1): 1-46 (1997) - 1996
- [j12]Michael Rathjen:
Monotone Inductive Definitions in Explicit Mathematics. J. Symb. Log. 61(1): 125-146 (1996) - [j11]Michael Rathjen:
The Recursively Mahlo Property in Second Order Arithmetic. Math. Log. Q. 42: 59-66 (1996) - 1995
- [j10]Michael Rathjen:
Recent advances in ordinal analysis: pi12 - CA and related systems. Bull. Symb. Log. 1(4): 468-485 (1995) - 1994
- [j9]Michael Rathjen:
Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM. Arch. Math. Log. 33(1): 35-55 (1994) - [j8]Edward R. Griffor, Michael Rathjen:
The strength of some Martin-Löf type theories. Arch. Math. Log. 33(5): 347-385 (1994) - [j7]Michael Rathjen:
Proof Theory of Reflection. Ann. Pure Appl. Log. 68(2): 181-224 (1994) - 1993
- [j6]Michael Rathjen, Andreas Weiermann:
Proof-Theoretic Investigations on Kruskal's Theorem. Ann. Pure Appl. Log. 60(1): 49-88 (1993) - [j5]Michael Rathjen:
How to Develop Proof-Theoretic Ordinal Functions on the Basis of Admissible Ordinals. Math. Log. Q. 39: 47-54 (1993) - 1992
- [j4]Michael Rathjen:
A Proof-Theoretic Characterization of the Primitive Recursive Set Functions. J. Symb. Log. 57(3): 954-969 (1992) - 1991
- [j3]Michael Rathjen:
Proof-theoretic analysis of KPM. Arch. Math. Log. 30(5-6): 377-403 (1991) - [j2]Michael Rathjen:
The Role of Parameters in Bar Rule and Bar Induction. J. Symb. Log. 56(2): 715-730 (1991) - 1990
- [j1]Michael Rathjen:
Ordinal notations based on a weakly Mahlo cardinal. Arch. Math. Log. 29(4): 249-263 (1990)
Conference and Workshop Papers
- 2019
- [c7]Lorenzo Carlucci, Leonardo Mainardi, Michael Rathjen:
A Note on the Ordinal Analysis of \mathbf RCA_0 + \mathrm WO(\mathbf σ ) RCA 0 + WO ( σ ). CiE 2019: 144-155 - 2013
- [c6]Robert S. Lubarsky, Michael Rathjen:
Realizability Models Separating Various Fan Theorems. CiE 2013: 306-315 - 2012
- [c5]Bahareh Afshari, Michael Rathjen:
Ordinal Analysis and the Infinite Ramsey Theorem. CiE 2012: 1-10 - 2007
- [c4]Michael Rathjen:
Theories and Ordinals: Ordinal Analysis. CiE 2007: 632-637 - [c3]Robert S. Lubarsky, Michael Rathjen:
On the Constructive Dedekind Reals: Extended Abstract. LFCS 2007: 349-362 - 2006
- [c2]Michael Rathjen:
Models of Intuitionistic Set Theories over Partial Combinatory Algebras. TAMC 2006: 68-78 - 1995
- [c1]Michael Rathjen:
The Higher Infinite in Proof Theory. Logic Colloquium 1995: 275-304
Parts in Books or Collections
- 2012
- [p2]Michael Rathjen:
Constructive Zermelo-Fraenkel Set Theory, Power Set, and the Calculus of Constructions. Epistemology versus Ontology 2012: 313-349 - 2005
- [p1]Michael Rathjen:
Generalized Inductive Definitions in Constructive Set Theory. From sets and types to topology and analysis 2005
Informal and Other Publications
- 2021
- [i3]Michael Rathjen:
No speedup for geometric theories. CoRR abs/2105.04661 (2021) - 2020
- [i2]Anton Freund, Michael Rathjen, Andreas Weiermann:
Minimal bad sequences are necessary for a uniform Kruskal theorem. CoRR abs/2001.06380 (2020) - 2019
- [i1]Martin Krombholz, Michael Rathjen:
Upper bounds on the graph minor theorem. CoRR abs/1907.00412 (2019)
Coauthor Index
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